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Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Getting Your Bearings, The Sizes of Things
Math Review
The Constellations
Constellation List
Star Maps
Star Songs
How Earth and Sky Work- Effects of Latitude
How Earth and Sky Work -The Effect of
Time
Positions of the Sun and Moon
Eclipse Tables and Map
History of Astronomy
-Ancient Times through Galileo
History Timeline
Calendars and Time
The Start of Modern Physics
Using Equations and Formulae
Chapter 8
Chapter 9
Illuminating Light
Solar System Overview
Chapter 10
Earth, Our Point of Reference
History of Earth
Comparative Planetology
Chapter 11
Test 1 Review
Test 2 Review
Final Review
THE VISIBLE UNIVERSE 2012
karen g
castle
2
Chapter I Getting Your Bearings, Math Skills and The Sizes of Things
Finding sizes: As part of the first assignment, you will be finding sizes of things. You might need to
find mass or radius or lifetime. The assignment is geared to your textbook, although you may use the
internet to find the information. Be very careful to get what is requested. Download and save the
Internet reference if you want to be able to show that the answer is correct.
Part of what we are learning is how to convert units and how to use a logarithmic plot. So don’t spend a
lot of time searching for the exact units (e.g. finding meters vs Earth radii).
Converting Units: We compare the sizes of objects in order to get a concept of the Universe. The term
size is somewhat vague. It might mean mass, radius, area, circumference, duration in time etc.
Generally these features are not interchangeable. They have different meanings and refer to different
features.
Even when we have comparable measurements e.g. lengths, the values all need to be in the same
units so that we can understand what is larger. If the information isn’t all in the same units, it is
necessary to convert it so that they can be compared. What if we don’t have the information in the
same units? It is necessary to convert them to the same units.
For the first homework, we will find a dimension: that is, a length, width, diameter etc. Other forms of
size, such as mass, area, or volume are useful, but not directly comparable. To decide whether you
have found the proper dimension, the values must be in units of length e.g. meters, miles, kilometers
etc.
There may not be one exact answer for each item. For example, you might be seeking the size of an
automobile. Possible answers would be the length of a Mini Cooper, about 97 inches long
0
0
(2.46x10 meters in scientific notation) and 55.4 inches (1.47 x10 meters) high. A Hummer H3 might be
0
6.7x10 meters long and about 1.85 meters high. We can convert the lengths or heights of the vehicles
to the same units to see which is larger. On the other hand, the mass of the auto, or the surface area
are different from one another and different from the length or height. They cannot be compared
directly. They need to be in the same units.
Units In science (and almost everywhere but the USA) the metric system is used. So lengths should
be in centimeters, meters, or kilometers. Time is usually in seconds. Mass would be in grams or
kilograms. In astronomy there are some other, unique, units you will be seeing. These include
8
11
Astronomical Unit – distance between the Earth and Sun=1.496x10 km=1.496x10 m
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15
Light Year(ly), distance light travels in a year=9.46x10 km=9.46x10 m
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16
Parsec(pc) = 3.26 light years= 206265 Astronomical Units=3.0856x10 km=3.0856x10 m
(a parsec is the distance of a body whose parallax is 1 second of arc)
Your book has quite a few relations between units (appendix and inside front cover). For example
100 centimeters (cm)=1 meters (m)
1000 meters (m) = 1 kilometers (km)
1 mile (mi)= 1.609 km
1 meter = 39.37 inches (beware, meter is abbreviated m and mile is abbreviated
mi)
It is handy to write down all the conversion factors in one place, like a page of your notebook, so you
don’t need to search..
Converting units does not change their meaning. But, as you know from algebra class, the only things
that can be done to a number without changing its value are to add 0 or to multiply by 1. To convert
multiply by 1.
This may sound useless, how can multiplying by 1 do anything at all? To convert units, you might use
any of the following. They are all equal to 1, since they are the same on the top and bottom.
Chapter I Getting Your Bearings, The Sizes of Things
1
3
3 9.4605x10 15 m
3 1 light year
1.4960x1011 m
1AU
3.0857x10 16 m
1km
1 in
4
3.937x10 in .0254 m
1 pc
All of these values are equally true, but each is most useful when the units of the denominator (bottom
of the fraction) are the same as the units of the value you want to convert, so that the units cancel.
Read through the examples to see how it works.
€
Example: Saturn’s orbit has a semimajor axis of 9.3539 AU. How large is the semimajor axis in
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meters? To get from AU to meters, look up 1 AU = 1.496x10 m
Since these values are equal, they can be placed, one over the other, to make a form of 1. How should
it be done? The units of the previous value (the AU) should be on the bottom, to cancel.
9.539 AU
Cancel the AU to get
"1.496 x 1011 m %
= 9.539AU x $
'
1 AU
#
&
= 9.539 x1.496 x 1011 m
= 1.427x1012 m
Example: Sirius is 2.7 parsecs away from the Sun. How far away is this in meters?
€
The parsecs cancel.
17
Example: The distance to Vega is 2.39x10 m. How many light years is that?
" 1 light year %
' , with the meters on the bottom to cancel the units. So
# 9.46x1015 m &
Multiply the distance by $
# 1 light year &
2.39 × 1017 m × %
(
$ 9.46 × 1015 m '
15
€ year &
# 2.39 × 1017 light
Since 9.46x10 was on the bottom of the fraction, we divide BY it to get
=%
(
15
9.46 × 10
$
'
= 25.26 light years
€
When you start, there is no equation. You just write the number and equate it to itself times ONE. You
can tell that the conversion is correct if the units (just the names like parsec or km) cancel top and
bottom. Find these “same” values from a textbook or the work book. You do not need to memorize the
number values.
Often, you will not find a single equation relating the original units to the final value. In that case, find
relations between the current units and some other, then between that unit and another, etc. etc. until
you have steps relating one unit to the next, without skipping any steps. In this case you will be
multiplying by 1 several times. It is generally better to write out ALL the terms, cancel the units (to be
certain that the correct values are being used) and only then to multiply all the values together.
Example: A football field is 300 feet. How many kilometers is that? Find the conversion factors to go
from the original units, step by step, to the units you want.
# 12inches & # 0.0254m & # 1km &
300feet × %
(×%
(×%
(
$ 1foot ' $ 1inch ' $1000m '
# 0.0254m & # 1km &
= 3600 inches × %
(×%
(
$ 1inch ' $ 1000m '
# 1km &
= 91.44 × %
(
$1000m '
= 0.09144km
Check yourself: Convert each of the following a) 1.7x10
Convert 13 Mpc to m d) 14kpc to m e) 3.4 ft to m
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inches to m
b) 14 yards to miles c)
€
Chapter I Getting Your Bearings, The Sizes of Things
2
4
11
b) 14yd x"$ 3ft %' x"$ 1mi %' = 7.95x10 −3 mi c)
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a) 1.7x10 inches=4.318x10 m
# 1yd & # 5280ft &
20
d) 14 kpc = 4.326x10 m
0
e) 3.4 ft = 1.04x10 m
€
Calculator Note: The order of multiplication and division doesn’t matter. On the other hand, many
calculators will need more parentheses than you might think.
Example: If you type 6/5x7 into a calculator, you get 8.4 not 0.171. The calculator will divide 6 by 5
and then multiply the answer by 7. To divide 6 by 5x7, you need to type 6/(5x7) or 6/5=/7=.
Scientific Notation; This is a style of numbers. Scientific notation does not change the information, but
does make it easier to compare values and eliminates the need to write out many zeroes.
In Scientific Notation the value is written as
a number between 1 and 9.9999 times an integer power of 10.
1
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4
So the following are written in scientific notation: 5x10 , 4.23x10 , 1.09 x 10 while the following are not:
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7
50, 43.9x10 , 0.00109 x 10 although these numbers represent the same values. When operating with
scientific notation, the easiest thing is to load the values (in whatever format) into your calculator, find
the answer, and then write the answer in scientific notation.
To put a number into scientific notation, move the decimal point until it is to the right of the first non-zero
digit and count how many places you have moved it. Then multiply by 10 to the power equal to the
number of places that you moved the decimal. If you moved the decimal to the left, making the number
smaller, then multiply by 10 to a positive power. If you moved it to the right, making the number larger,
then multiply by 10 to a negative power. If there is no decimal showing, it is past the last digit to the
right. For example
5234.=5.234x10
0.0034=3.4x10
3
-3
Calculator Note: Calculators express the power of 10 using a key that says EE or EXP or ee . The ee
key is usually a second function (above the actual keys). These keys tell the calculator that the next
number will be the power of 10 that is part of the number.
3
e.g. 5.234x10 is 5.234 EE 3 or 5.234 EXP 3
-3
3.4x10 is 3.4 EE -3 When you want to enter the -3, it is necessary to use the +/- key.
Things that don’t give the right answer include:
a) typing x10 as part of the number
x
b) using the e key or e key for a power of 10
c) using the - key to get a negative number.
Plotting: We want to plot the sizes of astronomical objects to compare them. The wide range of
sizes doesn’t usually fit on a single plot, so we use a logarithmic plot, like the following.
A logarithmic plot gives equal space to equal powers of 10, rather than giving equal space to equal
size intervals. The major divisions start at 1 times a power of 10. Numbers that are not exactly powers
3
5
of 10 (e.g. 4 x 10 , 3.8 x10 etc) are plotted between the major divisions. The tiny numbers 2, 3,5,8
show which mark to use for 2 times the power of 10 that is immediately below, 3 times, etc. The tic
marks show all of the multipliers (2x, 3x, 4x etc). They are not all labeled because there is too little
space.
To use the graph, each number must be in scientific notation first (a value between 1 and 9.999 times
an integer power of 10). Since the number is LARGER than the power of 10, its value will be plotted
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ABOVE the power of 10, at the position indicated by the leading number. For example 8x10 km
Chapter I Getting Your Bearings, The Sizes of Things
3
5
Sizes in Meters
1.0x10 0
1.0x10-1
1.0x10-2
1.0x10-3
1.0x10-4
1.0x10-5
1.0x10-6
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
1.0x10-7
8
5
3
2
1.0x10-8
8
5
3
2
1.0x10-9
8
5
3
2
1.0x10-10
1.0x10-11
1.0x10-12
1.0x10-13
1.0x10-14
1.0x10-15
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
1.0x1015
1.0x1014
1.0x1013
1.0x1012
1.0x1011
1.0x1010
1.0x109
1.0x108
1.0x107
1.0x106
1.0x105
1.0x104
1.0x103
1.0x102
1.0x101
1.0x10 0
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
1.0x10 30
1.0x10 29
1.0x1028
28
282
1.0x1027
1.0x1026
1.0x1025
1.0x1024
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
1.0x1023
8
5
3
2
8
5
3
2
1.0x1022
8
5
3
2
8
5
3
2
1.0x1021
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
Chapter I Getting Your Bearings, The Sizes of Things
1.0x1020
1.0x1019
1.0x1018
1.0x1017
1.0x1016
1.0x1015
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
8
5
3
2
4
6
9
appears above the 1x10 line at the value 8. The value 1.2x10
19
but below the 2x10 line.
19
appears slightly above the 1x10
19
line,
When you plot the values you have found on the logarithmic graph provided and label them with the
name of the object. The vertical coordinate on the plot is the size of the object in kilometers. The
horizontal coordinate on this graph has no meaning (although it does on other graphs).
Theory Note: How is spacing of the numbers decided? Every positive number can be represented by
10 raised to some power. This power is called the logarithm of the number. The power is not usually an
integer. The spacing is determined by this power. So, for example,
log (4)
.602
=10
, so the 4 is about 0.6 of the way from the bottom of the interval to the top. The
4=10
spacing of the small marks takes the logarithms into account.
Math Notes
Order of Operations
Do whatever is within parentheses first. Then:
Raise to powers (i.e. evaluate the effect of the exponent)
Multiply and divide (order doesn’t matter)
Add and Subtract (order doesn’t matter between these)
So, for example
3
2
6 + 9 +4x5/17 = ?
would be evaluated as follows.
Do powers first, then multiplication and division, then addition and subtraction.
(63) + (92)+{4x(5/17)} or (63)x(92)+{(4x5)/17}
=216 + 81 +20/17= 297+20/17 =297+1.176=298.176
When using a calculator, be prepared to use parentheses in more places that you might expect. For
example, the expression, 6x 7 should come out as 3.5. The order of multiplication and division doesn’t
4x 3
matter, but the expression includes dividing by 3. A calculator may give (6x7/4)x3 = 31.5, depending on
how the information is entered. The calculator needs to be told explicitly to divide by 3.
Exponential Notation
The symbols 103, 1E3, and 10**3 all mean 10 to the third power i.e. 10 x 10 x 10. The first way of
writing is used if the writer can do superscripts, the other ways are used in some computer notations
where superscripts are not available
More generally 10n means 10 multiplied together n times,
i.e. 10x10x10...x10 where there are n repetitions of 10
(or equivalently 1 with n zeroes following it.).
To multiply together two numbers of the form 10n x 10m, the exponents are added, e.g.
10n x 10m=10m+n
Similarly, 145 means 14 x 14 x 14 x 14 x 14 = 537824 not 14x105.
A negative exponent, means 1 divided by the number raised to the power given. e.g.
10-1 means 1/10
2
2-2 means 1/2 =1/4
10-2 means (1/10) multiplied together twice, i.e.
2
10-2 =1/10 = (1/10) x (1/10) = 0.01
-4
Similarly,
17-3= 1/(17 x 17 x 17) = 2.035x10 = 0.0002035.
Chapter I Getting Your Bearings, The Sizes of Things
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The rule of adding the exponents when multiplying numbers of the form 10-n x 10m holds so
10-n x 10m =10-n+m =10m-n
or subtract the exponent on the bottom when dividing. For example
m
n
m-n
10 /10 =10
In math, two negatives cancel (or two wrongs make a right, if you like), so
m
m – (-n)
m +n
-n
10 /10 =10
=10
Examples
109/ 1012 = 10 9-12 = 10 –3
109/10-12 = 109-(-12) =1021
Addition/Subtraction The calculator will take any combination, but there is no simple way to add
exponential numbers, by hand. You need to either write them out explicitly or factor them e.g.
102+104= 100+10000=10100
=102 x (1+102)=102 x (1+100)= 102 x (101)=10100
Computing with Scientific Notation and Similar Forms
Because the order of multiplication and division doesn’t matter, scientific notation can be used in
computation as follows.
6
9
6+9
15
16
3.1x10 x 7.5x 10 = 3.1 x 7.5 x 10
= 23.25 x 10 =2.325 x 10 in scientific notation. It is
necessary to increase the exponent to compensate for decreasing the value 23.25 to 2.325 and
increasing the exponent.
It is NOT necessary to separate the powers of 10 from the rest of the computation. It is helpful if you
are doing the computation by hand, because it is easy to compute the powers of 10 and estimate the
rest. In the computation about, the 3x7 part could be estimated as 21. That would not be final answer,
but it would give a rough idea of the result.
Solving Equations
Often we have a formula where we know values for some, but not all, of the variables. For example
Distance =Rate xTime
Distance= 340 kilometers, Time= 3 hours
The goal is to rearrange the values so that an unknown value appears on one side, alone, and only
known values appear on the other. The way to do this without destroying the information embodied in
the equation is to use
EQUAL TREATMENT
for both sides of the equation
You can do the following without making an equation untrue:
Substitute a numerical value for a variable, if you know the value
Multiply or Divide by something, both sides (using zero here is legal, but it destroys the
process)
Add or Subtract something, both sides
Raise something to a power (like square it, take the square root)
Clear parentheses, for example a(b+c) = ab + bc
and you should do one or another of the above (or several) if it helps to get all the known things on one
side, and the unknown things on the other.
Looking back at the problem,
Distance =Rate xTime
Distance = 340 kilometers, Time= 3 hours
Chapter I Getting Your Bearings, The Sizes of Things
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We know the distance and the time and want to find the rate. So divide both sides by Time, to get rate
by itself
(1/Rate) x Distance =Rate x Time x (1/Rate)
The point was to be able to cancel the Rate, so we do to get
(1/Rate) x Distance =Rate x Time x (1/Rate)
Distance/ Time = Rate
Now it is easy to substitute, (Distance = 340 kilometers, Time= 3 hours)
340 km/3 hr = Rate
113.33 km/ hr = Rate
Algebra Advice
Solutions in algebra are not very intuitive. Don’t expect to know the answer automatically, no matter
how brilliant you are. It is rather like fixing a car or cooking. No matter how smart you are, it still takes all
the steps and a bunch of time. It doesn’t mean that you are dumb or bad at math. It just works slowly
and systematically. It is best to write out EVERY step completely. Be sure that each line is a repetition
of a true equation. That way, you can understand what you have done if you come back.
Not every legal thing you may do will help isolate the unknown. If it doesn’t help, it may be necessary
to start again. Even if it seems to have helped, it may be worthwhile to put the problem away.
A good way to check your work is to put the answer aside, separate from the problem. Come back to it
when you have not thought about it for a while. Redo the problem. NOW compare your results. If they
are different, at least one must be incorrect. If you are working with a friend, compare methods, each
reading the other person’s. Or read the work out loud to someone, even if they have not done the
problem. It will make you go over the information slowly and often help you to notice an error. It is hard
to read your own work and find the error. We all want to be right and that gets in our way as we look at
our own results.
Uncertainty and Number of Significant Figures
Most numbers we use are the results of measurements. That means that they are not perfectly
accurate. Unfortunately not all textbooks tell you how accurate the values are and it is not true that the
-9
last digit is the only one that is uncertain, Consider a value like 3.88x10 . The range of values really
-9
-9
might really be from 4.03 x10 to 3.5x10 with probability 95% (typically the exponent would not
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change). Another way that this can be written is 3.88 x10 ( +0.15, -0.38, 2σ). There is no way for you
to know the uncertainty is unless the author specifies it. In this case, we would say that the value has 1
significant figure, since the range of values from largest to smallest leaves only one digit unchanged.
If we don’t have detailed information about the measurement uncertainty, the number of significant
figures is used to estimate the error. When computing with measurement values, you should get a
result only as good as the LEAST accurate of the numbers included. If the only operations are
multiplication and division, and the values are all expressed in scientific notation, the number of figures
in a number is the number of digits in the number before the power of 10. The power of 10 does NOT
affect the number of significant figures. If the number is NOT in scientific notation, leading zeroes do not
count as significant figures, but trailing zeroes do. Examples:
-2
0.09 has 1 significant figure (9. x 10 )
0.010 has 2 significant figures since the 0 following the 1 indicates that you know the next digit. You
-2
could write it as 1.0 x 10 . The leading zero(s) indicate the power of 10, but is (are) not considered to
be significant figures
9
9.87 x 10 has 3 significant figures
9
Thus, the result 0.09 x 0.010/9.87x10 = 9x10
the least accurate value in the computation.
-14
should have ONLY 1 significant figure, the same as
Chapter I Getting Your Bearings, The Sizes of Things
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9
If addition or subtraction is involved in a computation, the numbers need to be written out, and digits
should be kept so long as they are the result of known values.
3
Example 3.24 x 10 +204+62.6=
Adding 3240 ( actually we don’t know the 0, but it is needed to keep the columns straight)
204
62.6
3506.6 This value does not include the correct number of significant figures. If we write it in
3
3
scientific notation the result becomes 3.5066x10 , with all the digits, and 3.51 x10 with the correct
number of digits. The two 6’s resulted from addition of some uncertain values. The final answer was
rounded up to get the best value
Conversion Factors
1 meter = 39.37 in (meter is abbreviated m)
1 foot = 12 in
1 in = 2.54 cm
1 mile = 1.609 km
1 statute mile=5280 feet (this is the normal kind of mile, it would be abbreviate mi, NOT m)
1 nautical mile= 6080 feet
1 nautical mile= 1.853 km
1 m = 100 cm
1 km = 1000 m
–6
1 µ = 10 m ( the symbol µ , like m in the Greek alphabet, stands for micron unit)
-9
1 nm = 10 m
–8
1 Å = 10 cm=10-10 m (the symbol Å stands for Ångstrom units)
8
1 AU = 1.496x10 km (AU stands for Astronomical Unit, the average distance from the Earth to the
Sun)
12
1 ly = 9.46x10 km (ly stands for light year, the distance that light would travel in a year)
1 pc = 3.26 ly
13
1 pc = 3.0857 x10 km
(pc stands for parsec, the distance at which parallax shift due to the observer moving by 1 AU is one
second of arc)
3
1 kpc = 10 pc
6
1 Mpc = 10 pc
Triangles
If you know two sides and one angle,
you can finish drawing the triangle.
Which means, the triangle is known.
e.g.
If you know all three sides, you can also finish the triangle, i.e. draw
and stick it together in only one way.
So you know the entire triangle
On the other hand, if you know all the angles, you know the shape of
the triangle, but not its size. Triangles with the same shape as one
another are called similar, like the following three triangles.
Chapter I Getting Your Bearings, The Sizes of Things
8
10
The angles in any plane triangle always add up to 180 degrees.
Angles
o
o
360 in a circle, 180 in the angles of a triangle or on one side of a straight line
o
1 =1 degree=60' ( minutes of arc)
1'=60" (seconds of arc)
Areas
Triangle Area = 1/2 Base x Height
Rectangle Area = Base x Height
Circle
Area = π Radius 2, where π = 3.14159...
The circumference of a circle is Circumference = 2 π Radius. The number of degrees in a circle is 360.
Trigonometry, just so you know
A special, useful class of triangles is the right triangle. Since one of the angles in it is always 90
degrees, the right angle, and there are 180 degrees total, there are 90 degrees left among the other two
angles. Once one of the angles is known, the other is simply the remainder of the 180 degrees.
Since the shape of a right triangle is known once one of the smaller angles is known, we can
understand the relations between the lengths of the sides. The relations are tabulated as the functions
shown above. The ratios of the lengths of the sides can be found in books or on scientific calculators.
Be sure that the calculator is in degrees mode to use it to find a trigonometric function.
o
One more quick trick. If an angle is smaller than about 10-15 , then sine or tangent of the angle is about
the same as the size of the angle in radians.
Angles
o
o
360 in a circle, 180 in the angles of a triangle or on one side of a straight line
o
1 =1 degree=60' ( minutes of arc)
1'=60" (seconds of arc)
o
1 radian = 57.295...
o
2 π radians =360
Areas
Triangle Area = 1/2 Base x Height
Rectangle Area = Base x Height
Circle
Area = π Radius 2, where π = 3.14159...
Sphere
Area = 4π Radius 2
The circumference of a circle is Circumference = 2 π Radius.
Chapter I Getting Your Bearings, The Sizes of Things
9
11
Chapter 2 The Constellations
The constellations are formally named patterns and areas of the sky. Ancient people named patterns they
found from their locations. Different peoples found very different patterns and named them differently.
Even the choice of stars to combine varied. Many of the constellations we use today first started with the
Babylonians and were modified by the Greeks. The Romans seem to have adopted the Greeks’ apprach. During the Dark Ages in western Europe, the Islamic world maintained the knowledge of astronomy
developed by the Greeks. Most of our common star names are Arabic names developed during this time.
Not every visible star was used to make the named pattern. The Greeks and Romans had no names for
stars or patterns too far south to be seen from the Mediterranean area. Native people in Africa, Polynesia
and Australia had star and star pattern names, but we have not adopted them.
Europe awoke from the Dark Ages and became reacquainted with the Greeks’ knowledge starting around
1000CE (Common Era). The works of Plato and Aristotle were translated into Latin (from Arabic). These
authors were more advanced than the Europeans of the day. So they were studied, not challenged.
By the 1600’s and 1700’s CE, astronomers realized that there were unnamed parts of the sky and that
use of the telescope would lead them to find increasing numbers of stars. They proceeded to name
constellations covering all regions of the sky. Some of the names they chose, such as Telescopium, attest
to the modern origin of these constellations.
Astronomers extended the definition of a constellation to include a region of the sky and any stars
found within the region. The stars making up the traditional pattern (if any) are included in the boundaries,
as are any additional objects found within the boundaries. These constellation boundaries are shown in
Figure 2-5.
A total of 88 constellations cover all directions. These constellations are used by astronomers planetwide.
Stars in a constellation are not normally associated in three dimensional space.
Other apparent star groupings are called asterisms. The stars in an asterism can belong to one or
several constellations. Asterisms can be likened to nicknames or names for neighborhoods. Many,
including the Big Dipper, Little Dipper, and Summer Triangle are very famous. Additional asterisms can
be created at will, but changing constellations requires the decision of the International Astronomical
Union (IAU).
You will be learning to recognize some of the more prominent constellations visible from the USA. The list
of constellations and asterisms we may cover follows. After we have covered each constellation or
asterism in class, you will be responsible to know
st
a) Official name of the constellation (or asterism) – 1 column
st
b) Official meaning of the name (not what we think it looks like) –1 column
nd
c) Name(s) of first magnitude and other stars in the constellation –2 colunm
(Star names are bold. The other information in this block is for your observing
pleasure)
d) Find the constellation or any of the stars on a star map with no lines
e) Circle the stars in the constellation
f) Read the Right Ascension and Declination of a star or constellation from the map.
In a test or quiz There will be no lines, no numbers, but tic marks to indicate where the lines
would be.
The data in the last column of the tables expresses coordinates of (roughly) the middle of the constellation.
There is nothing official about them. They are not the coordinates of any particular star in the constellation.
Their purpose is to allow the reader to find the constellation (or to explain to another where it is) if he had
no idea. There is no reason to memorize these values if you can find the constellation on a map. Do NOT
use these coordinates for stars.
You will be using these names and positions in some of the exercises concerning what can and cannot be
seen from different locations and at different times. As you use these stars, you will be expected to be able
to find them on a map without lines.
Constellations retain their positions relative to one another, but their position relative to the horizon
changes as the Earth spins. So it is handy to use one to find another, rather than to count on using the
horizon or land-based references to find them.
Chapter 2
Constellations
1
12
Name/
meaning
Andromeda
(And) name
(daughter
of
Cassiopeia)
Aquila
(Aql) eagle
Auriga
(Aur)
charioteer
Boötes
(Boo) herdsman
Cancer
(Cnc)
crab
Canis Major
(CMa)
large dog
Canis Minor
(CMi) small dog
Cassiopeia
(Cas)
Her name
(a queen)
Cepheus(Cep)
His name(a king)
Corona
Borealis (CrB)
northern crown
Cygnus
(Cyg)
swan
Delphinus
(Del) dolphin
Draco (Dra)
dragon
Gemini (Gem)
twins
(Castor and
Pollux )
Hercules
(Her)His name
Leo
(Leo)
Lion
Lepus
(Lep) hare
Libra (Lib)
balance scale
Chapter 2
Features and Bright Stars
Approx
Location
M31 Andromeda Galaxy at RA
00 hr 42.7 min, Dec
+41°16', Naked Eye
Andromeda's head is shared with Pegasus
And (Almak) Bright Binary K2 and A0, Eastern "foot"
Aquilae is Altair, First Magnitude from Flying Eagle,
Southernmost part of Summer Triangle
Aurigae is Capella First Magnitude
M36(RA 5 hr 36.1m, Dec +34°8') and nearby M37, M38
Open Clusters
Boötis is Arcturus, find Using Big Dipper Handle, Kite
Shaped, is triple, incl. visual Binary "Pulchrissima"
M 44, Praesepe (RA 8 hr 40.1m, Dec +19°59') a star
cluster best seen in binoculars
Canis Majoris is Sirius brightest apparent , Double with
White Dwarf
M41(RA 6 hr 47.0m, Dec -20°44') open cluster
Canis Minoris is Procyon first magnitude, with white
dwarf companion
Relatively bright is a Variable star changing from 1.6 to3.
mag (middle of W)
M103 (RA 1 hr 33.2m, Dec +60°42') open cluster is near
Tycho Brahe found a Supernova here
Not Bright,
Cepheii is variable and is distance
benchmark
T Cor Bor, (not naked eye) has brightened twice(1945,
1866) to mag 2, drops to 15 near Cor Bor
RA 1 hr ,
Dec +40 °
Cygni is Deneb, "bird's tail", first Mag is northernmost,
Southern end ( ) is Albireo fine blue and yellow binary
North America Nebula 3 ° E of Deneb
East of Summer Triangle,
No bright stars, but distinct pattern
Extends between Ursa Major and Ursa Minor, all faint stars
RA 20 hr 30
min Dec +40°
RA 19hr 30min
Dec +5°
RA 5 hr 30 min
Dec +40°
RA 15hr 30min
Dec +30°
RA 8 hr 30 min
Dec +20°
RA 7 hr
Dec-25°
RA 7 hr 30 min
Dec + 5°
RA 1 hr
Dec +60°
RA 22 hr
Dec +70°
RA 15 hr 45
min Dec + 30°
RA 20 hr30min
Dec +15°
RA 10 to 21 hr
Dec +65°
Geminorum, the fainter, is Castor, is Westward and RA 7 hr
Dec +25°
triple,
Geminorum, the brighter, is Pollux is Eastward,
both first magnitude
M35 (RA 6 hr 8.9m, Dec +24°20')
M13 (RA 16 hr 41.7m, Dec +36°28') fine globular cluster
RA 17 hr
Dec +30°
Leontis is Regulus, first magnitude, the Stella Regina for RA 11 hr
Dec +17°
Greeks, many occultations,
Leontis is Denebola, Arabic for "Lions Tail"
M65(RA 11 hr 18.9m, Dec +13°05') Spiral Galaxy
M66(RA 11 hr 20.2m, Dec +12°59') Spiral Galaxy
M95(RA 10 hr 44.9m, Dec +11°42') Spiral Galaxy
M96(RA 10 hr 46.8m, Dec +11°49') Spiral Galaxy
No bright stars, below Orion
RA 5 hr 30 min
M79 (RA 5 hr 24.5m, Dec -24°33')rich globular star cluster Dec -20°
Faint stars, was part of Scorpius (a claw), renamed in RA 15 hr,
honor of Augustus Caesar for justice and reform of Law
Dec-15°
Constellations
2
13
Lyra (Lyr)
lyre
Monoceros
(Mon) Unicorn
Orion (Ori)
name
(a hunter)
Pegasus (Peg)
His name,
(winged horse)
Perseus
(Per)
His name
(a hero)
Pisces (Psc)
fish
Sagittarius
(Sgr)
archer
(anatomically a
centaur)
Lyrae is Vega, first magnitude; will be pole star in ~ RA 19 hr,
Dec 38°
13,000 years, Lyrae is eclipsing binary, with gas shells
M57 (RA 18 hr 53.6m, Dec +33°2')planetary nebula
Faint, between Orion and Canis Major
RA 7 hr
Dec -5°
RA 5 hr 30 min
Orionis, Betelgeuse, is reddish
Dec 0°
Orionis, Rigel, is a bluish system of five stars
M42 (RA 5 hr 35.4m, Dec -5°27' diffuse nebula, naked eye
No first magnitude stars, Large square with stars interior, RA 23 hr,
Looks like Baseball diamond
Dec +20°
M15 (RA 21 hr 30.0m, Dec +12°10') globular cluster
RA 3 hr 30 min
is Algol an eclipsing binary with 2.87 day period
Double Cluster h and
young open clusters in Milky Way Dec +45°
NGC 869 (RA 2 hr 19m, Dec +57°09') =h Persii
NGC 884 (RA 2 hr 22m, Dec +57°07') = Persii
All faint stars.
RA 1 hr,
Dec +10°
Trifid Nebula = M20=NGC6514
RA 19 hr
(RA 18 hr 2.6m, Dec -23°02') diffuse nebula
Dec-25°
Lagoon Nebula=M8=NGC6523
(RA 18 hr 3.8m, Dec -24°23') diffuse nebula
Omega Nebula = M17=NGC6618
(RA 18 hr 20.8m, Dec -16°11') diffuse nebula
Scorpius
Scorpii is Antares Temperature~3500°K, double RA 16 hr 45
(Sco)
M4=NGC6121 (RA 16 hr 23.6m, Dec -26°32') globular min Dec-30°
scorpion
cluster
M6=NGC6405 (RA 17 hr 40.1m, Dec -32°13') open cluster
M7=NGC6475 (RA 17 hr 53.9m, Dec -34°49') open cluster
Taurus
RA 4 hr 30 min
Tauri is Aldebaran, about 3000°K
(Tau)
Dec +15°
Pleiades=M45, open cluster (RA 3 hr 47.0m, Dec+24°07')
bull
M1=Crab Nebula ,Supernova remnant
(RA 5 hr 34.5m, Dec+22° 01')
Hyades naked eye V shape, nearby galactic cluster
Ursa Major
Extends from
Ursa Maoris is Dubhe, pointer nearer Polaris (double)
(UMa)
Ursa Majoris is Merak, the other pointer, a single A1 star RA 8 -14 hr
great bear
Mizar, at the bend in the handle of the dipper, is triple. The Dec +60°
visible dimmer companion Alcor (the rider) is binary as well
Ursa Minor
Ursa Minoris is Polaris (other name Cynosura), variable RA 16 hr
(UMi) small bear by 0.1 magnitude with 31.97 day period
Dec +80°
Virgo
Virginis is Spica, "ear of grain". Large cluster of distant RA 13 hr
(Vir) virgin
Dec +0°
galaxies in constellation
Asterisms: Summer Triangle (Deneb, Altair, Vega), Big Dipper (in Ursa Major),
Little Dipper (in Ursa Minor), and Winter Triangle (Betelgeuse, Procyon, Sirius)
Chapter 2
Constellations
3
14
UMi
Cam
Dr a
Cep
22h
60°
20h
60°
18h
60°
16h
60°
14h
60°
12h
60°
10h
60°
8h
60°
6h
60°
4h
60°
2 h Cas
60°
UMa
Lyn
Lac
Cyg
V ul
Peg
20h
30°
18h
Her
30°
CrB
16h
30°
Boo
14h
30°
Com
12h
30°
Sg e
22h
0°
A ql
20h
0°
A qr
10h
30°
1 8 hOph
0°
Se r
16h
0°
8h
30°
Gem
A nd
6h
30°
Tri2 h
30°
4h
30°
Tau
A ri
Cnc
Leo
Del
Eq u
A ur
LMi
Lyr
22h
30°
Per
CVn
Psc
CMi
14h
0°
V ir
12h
0°
10h
Se x
0°
8h
0°
Mo n
6Ori
h
0°
4h
0°
2h
0°
Cet
Sct
Crt
Lib
Cap
PsA
22h
-3 0 °
20h
-3 0 °
Mic
Sg r
18h
-3 0 °
Sco
16h
-3 0 °
CrA
Tuc
Tel
20h
-6 0 °
Pav
14h
-3 0 °
Lu p
Gr u
Ind
22h
-6 0 °
Crv
A ra
18h
-6 0 °
12h
-3 0 °
8h
-3 0 °
Pu p
Pyx
2h
-3 0 °
For
Scl
Cae
14h
-6 0 °
Cru
12h
-6 0 °
10h
-6 0 °
Ho r
Car 8 h
-6 0 °
Pic
6h
Do r
-6 0 °
Ph e
4h
Re-6
t 0°
2h
-6 0 °
V ol
Men
Cha
Figure 2-1 Entire Sky, Mercator Projection with Labels
Constellations
4h
-3 0 °
V el
A ps
Chapter 2
6h
-3 0 °
Col
Cen
Mus
Oct
Er i
CMa
10h
A nt -3 0 °
No r
16h
-6 0 ° Cir
TrA
Lep
Hya
4
Hyi
15
Figure 2-2 Entire Sky, Mercator Projection No Labels
Chapter 2
Constellations
5
16
Figure 2-3 Northern Hemisphere with Labels
Chapter 2
Constellations
6
17
Figure 2-4 Northern Hemisphere No Labels
Chapter 2
Constellations
7
18
UMi
Cam
Dr a
Cep
Cas
UMa
Lyn
Lac
Cyg
Her
CrB
Tri
Com
Gem
Sg e
Del
A ri
Psc
CMi
Se r
Oph
Ori
Se x
V ir
A qr
Tau
Cnc
Leo
A ql
A nd
Boo
V ul
Eq u
A ur
LMi
Lyr
Peg
Per
CVn
Mo n
Cet
Sct
Crt
Lib
Cap
PsA
Crv
Sg r
Pyx
A nt
CrA
Lu p
Gr u
Tel
Ind
Pav
A ra
Pu p
Col
V el
Cir
Do r
Re t
V ol
Men
Cha
Figure 2-5 Constellation Boundaries (with Milky Way shaded)- Entire Sky
Constellations
Ph e
Pic
Car
Cru
Mus
Oct
Scl
Ho r
A ps
Chapter 2
For
Cae
Cen
No r
TrA
Er i
CMa
Sco
Mic
Tuc
Lep
Hya
8
Hyi
19
Figure 2-6 Southern Hemisphere with Labels
Chapter 2
Constellations
9
20
Figure 2-7 Constellations of the Zodiac, the Constellations Along the Ecliptic
Chapter 2
Constellations
10
21
Studying the Constellations
Don’t expect to ignore the constellations until the day before the test and then read and remember the
maps. Do repeat the constellations several times a week, if not every day. It will only take a few minutes.
Don’t just look at the constellations and hope they will sink in. Use as many of your senses as possible. Make lots of copies of the blank maps. As we learn a few more constellations in class, study them, then
fill in the blank map over and over until you can do it from memory. Start with the same parts each time,
so you can build on what you already know. The next time we learn a few more constellations, repeat the
process. Drawing the constellations involves you visually and kinesthetically (moving your body as you
draw). Say the names out loud and use the mnemonics or sing the constellation songs to involve your
aural (hearing) memory.
You should have two goals as you study the constellations, to do well on the tests and to learn the
constellations so that you can find them in the sky. These are somewhat different because the test will be
from the fixed maps, while the orientation of the constellations in the sky changes. What doesn’t change is the relative positions of the stars and constellations. So it is helpful to go from one recognizable
constellation to the next. This section shows how to go from the most obvious constellations to others.
The mercator projection is broken up as follows. The polar map has a separate sequence of
constellations.
UMi
UMi
Dra
Cep
Dra
Cep
2 2 h2 2 h
6 0 °60°
2020
hh
6060
°°
1188hh
6600°°
16 h
16 h
60 °60 °
Arc to
Arcturus
1 4h 1 4h
6 0° 6 0°
12h
60°
12h
60°
CVn
Cyg
30°
V ul
Peg
Peg
CVn
30 °
18h
Her
3108°h Her
30°
CrB
16 h
1 4h
Boo
CrB
30
°16 h
3 0° 1 4h
Boo
Com
30 °
3 0°
12h
30°
Del
22h
Eq u
0°
22h
0°
Aql
20 h
0°
Aql
1 8 hOph
0°
A qr
Sct
1 8 hOph
0°
Se r
16 h
0° Se r
16 h
0°
Lib
Sct
Cap
1 4h
0°
Vir
Crt
Crv
22h
-3Cap
0°
Mic
22h
PsA
Gru
-3 0°
20 h
-3 0 °
Gru
CrA
20 h
-3 0 °
Sgr
T uc
20 h
-6 0°
-6 0 °
Pav
-6 0°
Oct
16 h
-3 0°
18h
-30 °
Lib
1 4h
-3 0 °
Ara
18h
-60 °
T el
20 h
-6 0 °
Pav
16
Luhp
-3 0°
Sco
T el
CrA
22h
Ind
22h
18h
-30 °
1 0h
Se x
0°
16 h
Lu p
-6 0° Cir
T rA
-60 °
Aps 16 h
-6 0° Cir
T rA
1 4h
-6 0 °
-6 0 °
30°
30°
Ari
Tau
Ari
Mo n
8h
0°
Mo n
8h
-3 0 °
Pu p
1 0h
A nt -3 0 °
V el
1 0h
Pic
6h
-6 0 °
Pyx
Car 8 h
-6 0 °
-6 0°
6h
Ori
0°
12h
1 0h
Cha°
-60
-6 0 °
2h
0°
Cet
0°
Eri
6h
-3 0°
Col CMa
Cae
8h
-3 0 °
Pu p
2h
0°
Cet4 h
4 Lep
h
-3 0 ° For
6h
-3 0°
Col Ho r
Dor
4h
Re-6
t 0°
Men
Pic
6h
2h
Eri
-30 °
Scl
4h
-3 0 °
2h
-30 °
For
Ph e
Cae
-60 °
Ho r
Car 8 h
-6 0 °
-6 0°
Hyi
Dor
Ph e
4h
Re-6
t 0°
2h
-60 °
V ol
Mus
Men
Aps
Hyi
Cha
Oct
Chapter 2
Constellations
Scl
2h
VVelol
Cru
And
T ri2 h
3 04°h
30 °
4h
0°
Lep
Mus
1 4h
6h
0°
CMa
1 0h
A nt -3 0 °HyaPyx
12h
Cru Cen
-60 °
And
T ri2 h
4h
6h
30°
Psc
Ori
CMi
1 0h
Se x
0°
12h
-30 °
Per
Psc
8h
0°
12h
0°
Nor
Nor
Ara
18h
1 4h
Cen
-3 0
°
Tau
Per
Aur
Cnc
Hya
1Crv
2h
-30 °
2 h Cas
60°
CMi
Sco
Mic
Ind
T uc
Sgr
2 h4 h Cas
6 06°0 °
Gem
Crt
PsA
30°
Cnc
12h
0°
1 4h
0°
Vir
6h
8 h30 °
Gem
3 0°
Leo
20 h
0°
A qr
8h
1 0h 3 0 °
Leo
Del Sg e
Eq u
LMi
1 0h
3 0°
12h
30°
Lyn
Orient to
Orion
Aur
Com
Sg e
6h
4h
60
6 0 °°
UMa
LMi
Lyr
20 h Lyr
2030
h°
V ul
22h
2 2 h3 0 °
8 h6h
6 060
° °
Lyn
Summer Triangle
Region
Cyg
1 0h 8 h
6 0° 6 0 °
1 0h
6 0°
UMa
Lac Lac
Cam
Cam
11
22
Orient to Orion
1 Find Orion and note his stars
2 Follow OrionÕs belt south to
Canis Major, his large dog
Betelgeuse
Orion
Sirius
Rigel
Canis Major
3 Slide along OrionÕs Collar Bone
to Canis Minor, the smaller dog
4 Go Diagonally up Orion to the
Dancing Twins, Gemini
Castor
Gemini
Pollux
Canis Minor
Procyon
5 Go Straight up
OrionÕs B ody
to reach Auriga,
the Charioteer
Auriga Capella
6 Going West Along
OrionÕs B elt R eveals
Taurus
Taurus
Pleiades
star cluster
Aldebaran
Chapter 2
Constellations
12
23
7 Little Lepus Hides b eneath OrionÕs F eet
8 Questioning Leo follows Gemini
Leo
Lepus the Hare
9 Crabby Cancer lies between
Pollux and Leo
10 Monoceros, the secretive Unicorn
slinks behind Orion
Cancer the Crab
Monoceros
11 Perseus treds
on T aurusÕ H orn
Perseus
Chapter 2
Constellations
13
24
Arc to Arcturus
1 Find Big Dipper part of Ursa Major
2 Extend the curve of the Handle to
ARCTURUS , the first bright star
Big Dipper,
part of Ursa Major
Arc to Arcturus
..
3 Draw in Bootes, the Herdsman
Shaped like a Kite
4 Continue the Curve through Arcturus,
but straighten to
Speed to Spica
..
Bootes
Spica
Chapter 2
Constellations
14
25
5 Fill in Virgo, lying on her back
..
6 Corona Borealis Nestles Near Bootes
Corona
Borealis
Virgo
7 Leo lies above VirgoÕs Head
8 Scorpius and Libra lie below VirgoÕs Legs
Leo
Libra
Scorpius
Chapter 2
Constellations
15
26
Summer Triangle Region
2 Deneb is the tail of
Cygnus the Swan
1 Summer Triangle joins
stars from three constellations
Deneb
Vega
CygnusÕ head is in
the middle of the triangle
Altair
D
e
n
e
b
A
l
t
a
i
r
D
e
n
e
b
V
e
g
a
3 Altair is in Aquila the Eagle
A
l
t
a
i
r
V goes to C
y
e
g
g
n
a
u
s
4 Vega,brightest star in the triangle
is part of Lyra, the lyre
Aquila
D
e
n
e
b
A
l
t
a
i
r
Chapter 2
V goes to C
y
e
g
g
n
a
u
s
A L
q
u
i
l
a
Constellations
D
e
n
e
b
A
l
t
a
i
r
V goes to C
e
y
g
g
a
n
u
s
A
q
u
i
l
a
L
y
r
a
16
27
6 Libra, the scales stands where
ScorpiusÕ claws once were
5 ScorpiusÕ tail scoops south
of the Summer Triangle
Arcturus
Find Libra
on a line from
Antares to
Spica or Arcturus
Libra
Spica
Antares
Antares
Scorpius
the Scorpion
7 Sagittarius the Archer
follows ScorpiusÕ Tail
Sagittarius can
look like a teapot
Chapter 2
8 Sagittarius the Archer
is Supposed to be a Centaur
Sagittarius
Constellations
17
28
Chapter 2
Constellations
18
29
Polar Polka
tune of Beer Barrel Polka chorus
Roll out the Pole Star
We’ll have Polaris all night
Spin out the Mom Bear
She’ll put you all in a fright
Follow Merak to Dubhe, they’ll put you right on the pole
Always roll out the pole star and you’ll sail all right.
Point through Polaris, you will find Cephe’ us’ hat Keep on a’curving, to find where Cassiopeia’s at
If you are clever, Andromeda hides behind
Her mother’s chair where she’s chained and she’s stuck all night
If you would save her, look for Perseus her beau.
He stands awaiting right near Andromeda’s toes
Perseus comes riding upon his flying horse,
Pegasus squares up the family and makes the
story come out right.
Stars Near Orion
Sung to the tune of “Dry Bones”
The belt stars’ connected to the Big Dog
And the shoulder stars’ connected to the Little Dog,
The twins dance on the diagonal
And that’s the way of the stars. Refrain:
Them stars, them stars goin’ to wheel around
Them stars, them stars goin’ to rise and set, Them stars, them stars goin’ light the night Chapter 2
And that’s the way of the stars The head star points to the Chariot—eer
The Bull is charging the Orion’s shield And the Hare is curling up Un’ derfoot
And that’s the way of the stars. Refrain
The lion lurks left of Little Dog
The Crab crawls after Milky Ways
Unicorns’ utterly unseen And that’s the way of the stars
Refrain
Aldebaran bashes Betelgeuse
And Betelgeuse chases Capella
Capella coaxes Castor West
And that’s the way of the stars. Refrain
Castor partners Pollux
And Pollux pulls on Procyon
The puppy pleases Sirius
And that’s the way of the stars. Refrain
Sirius snips at Rigel
Regulus returns to questioning
The beehive buzzes the crabmeat
And that’s the way of the stars. Refrain
Summer Sky Mneumonics
Arc to Arcturus, bound up in Boötes
Constellations
19
30
Speed on to Spica sweet Virgo’s waistband
Curve back to Corona butting up to Boötes.
Traipse the Triangle where DAV goes to CAL
Swoop to southern Scorpius tail.
The sea nymphs did hear her and weren’t amused
They complained to Neptune, that they were
abused.
So Neptune took umbrage and went to their aid
Scorpius claws at Libra’s steady balance, While Sagittarius arches to pour tea on his tail
Hercules Huddles ‘tween herdsman and Vega, flying upended o’re Ophiuchus and snake
He stole poor Andromeda from her mother’s side
Behind Cassiopeia’s Double U, her daughter doth
hide
Andromeda’s so timid cause to rock she’s tied. She’s tied to the rock awaiting her fate
To be eaten by Cetus, who is lying in wait
The Sad Song of Cepheus et al
A’fore evil Cetus could rip out her patella
The hero Perseus heard of her dilemma
(To the tune of “On Top of Old Smokey”
Perseus was famous, quite famous afore
For slaying Medusa, a monster of yore
On top of the North Pole,
The small bear does roll
Perseus went to poor Cepheus and to him he said
“May I please save her lest, she end up dead?”
Sep’rated from Mo-ther
For safety of all
So what do you think that poor Cepheus did?
He said, “Please, please Mr Perseus, go save my one kid.” The Mom Bear points to him,
With stars in her back
Perseus said, “Yes, fine, but what’s the quid pro the quo?
If I can save her, can married we go?”
Old Merak and Dubhe
Will show you how to react
Continue on further to Cepheus the sad
“Of course, my dear Perseus,” quoth the worried dad,
“Just prevent her from being eaten and I will be glad.”
A king with a ha-at , he married for bad.
His bride Cassiopeia , who one daughter had
So Perseus he whistled, and forth came a horse,
Flying Pegasus arrived in a froth.
She’ll kick her poor hubby, in hi-s left ear
Because she’s so gorgeous, her daughter’s in fear
Armed with Medusa, her head in his hand,
And aboard swift Pegasus, he flew o’re the land
Her daughter Andromeda is lovely it’s true, And Ms Cassiopeia told all whom she knew.
Perseus succeeded in freeing the girl
And carried her off with skirts in a whirl.
Bragged about her own offspring, as a true peach
E’ en prettier than sea nymphs as Cassiopeia did
preach
The all were as happy, as happy can be
That this song is over and lived happ i ly.
Past Arcas’ pole star, Polaris by name
We find a fami- lee of mythical fame
Chapter 2
Constellations
20
31
Chapter 3 How Earth and Sky Work- Effects of Latitude
In chapters 3 and 4 we will learn why our view of the heavens depends on our position on the
Earth, the time of day, and the day of the year. We will explore views of the Earth, the sky, and an
observer as seen from space and as seen from the surface of the Earth.
Today we know that the Earth is a sphere
and we are tiny by comparison. The
distance to every other celestial body is
MUCH larger than the diameter of the Earth.
Because we are so much smaller than the
Earth, the Earth appears to take up half of
all the directions we can look
The Earth and the other planets orbit the
Sun, while stars are at various distances
and orbit the Milky Way galaxy. But we can
use the idea of the Celestial Sphere to
describe the appearance of the sky. The
Celestial Sphere is an imaginary sphere
surrounding the Earth. Stars, the Moon, the
planets, the Sun, galaxies etc appear to be
pasted on the Celestial Sphere. Straight up
from Earth’s north pole is the North Celestial
Pole. The Earth pole and Celestial Pole are
lined up and remain lined up. The same for
the Earth’s South Pole and the South
Celestial Pole.
The figure shows our relation to the Celestial Sphere. The observer stands on the Earth. The
patterned surface is the apparent (flat) surface of the Earth, bounding the half of the sky visible to
the observer. As the Earth spins, different parts of the Celestial Sphere may become visible. When
the Earth turns so that a body comes onto the visible half of the Celestial Sphere, we say that it
rises. When the Earth turns so that a body becomes blocked by the Earth, we say it has set. The
Sun has no effect.
We
define
the
zenith, the horizon,
and the celestial
meridian
to
describe what an
observer can see.
These
reference
points depend on
the
observer’s
position. As Earth
spins, the zenith
and
meridian
change
as
the
person moves with
the Earth.
Meridian
Circle through Zenith,
North Celestial Pole,
South Celestial Pole
Zenith
Direction Straight Up
from Observer
Observer
CAN see
North
Pole
Observer
South
Observer
Pole
CAN NOT see
Horizon
Boundary between
Visible and Invisible
We
have
been
considering
what
the observer can see. The Earth spins and the observer moves with it, changing what is visible.
The stars move but they do not go around the Sun or the Earth. Because stars are so far away,
none of their individual motions of the stars is noticeable. Astronomers measure stars’ motions by
photographing them and comparing their relative positions over many years.
Chapter 3
How Earth and Sky Work -The Effect of Latitude
1
32
Because the stars move slowly it is useful to define stars' positions and patterns on the Celestial
Sphere and to learn how the positions relate to their visibility. We do this using coordinates that are
similar to Latitude and Longitude on Earth (other planets, moons and the Sun are also assigned
their own Latitude and Longitude systems.
North Pole
Earth
So first review Latitude and Longitude as
On Earth
shown in the figure.
o
Meridians of Longitude
Latitude is zero at the equator and ±90 at the
Run N-S
poles. Longitude is zero at the Prime Meridian
They tell the E-W position
o
in Greenwich England. It goes East for 180
Starts at Greenwich, England
o
and west for 180 . The International Date
o
Lines is approximately at the 180 line.
North Pole
The coordinates for the Celestial Sphere are
called Right Ascension and Declination.
They are similar to latitude and longitude on
the Earth. Each location on the Celestial
Sphere, that is each direction in the sky, can
be identified by its Right Ascension and
Declination.
South Pole
Earth
Parallels of Latitude
Run E-W
They tell the N-S position
Starts at the Equator
South Pole
On Celestial Sphere
Meridians of Right Ascension
Run N-S
They tell the E-W position
Start at Vernal Equinox
Run Parallel to Longitude Lines
North Pole
South Pole
North Celestial Pole
North Pole
Parallels of Declination
Run E-W
They tell the N-S position
Start at the Celestial Equator
Line up with Earth Latitudes
South Pole
South Celestial Pole
We think of the Celestial Sphere as fixed and the Earth spinning. As the Earth moves orbits and
spins, the Earth’s poles remain aligned with the poles of the Celestial Sphere and the parallels of
latitude remain aligned with the parallels of declination. Meridians of longitude and of Right
Ascension are parallel, but there is no one-to-one alignment.
You may be wondering how the imaginary Celestial Sphere fits with the overall concept of the
Universe, where the Earth orbits the Sun. The overall concept is in the figure below.
Chapter 3
How Earth and Sky Work -The Effect of Latitude
2
33
The Celestial Sphere is so large that the Earth's orbital motion is insignificant by
comparison.
The Earth moves in three dimensions, but to make it easier to draw, we will consider the
appearance two dimensions at a time. First we will consider the view from the right of the image.
When viewed from this direction, we see the effect of latitude on what can EVER be viewed.
Then we will look from above the North Pole of the Solar System. This will tell what can be seen at
a given time and date, but will ignore
the effect of latitude. The visibility
curves at the end of chapter 4,
combine both effects.
In each
situation, we will learn to compute what
can be seen.
Finding the Effect of Latitude
Latitude on the Earth (or another
object) is the angle between the
direction to a location on the object and
the equator of that object.
Chapter 3
How Earth and Sky Work -The Effect of Latitude
3
34
Let’s zoom out away from the Earth and the Celestial Sphere and see what happens as the Earth
spins (every 23 hr 56 minutes) and the Celestial Sphere stays still, the observer and her/his
horizon and meridian are carried along. Some stars rise and set, others are always seen.
Even though the Earth is really spinning, the appearance is that the sky is moving. If the figure
were redrawn to show the Celestial sphere moving, it would appear as follows.
In 12 hours, the sphere moves half way around. Ignoring the depth, the stars, the Sun, the Moon
and the planets appear to move horizontally from one side of the figure to the other, keeping the
same declination. Over the next 12 hours they move back to their original positions. Bodies at
some positions remain visible the entire time (circumpolar for this latitude); others remain invisible
(never seen); yet others change from visible to invisible. Bodies at these positions are said to “rise
and set.”
These pictures show the apparent motion of the sky, but do not provide a way to compute whether
a star will be visible all the time, some of the time, or none of the time. To find this, we need to
relate the declination horizon position on the sky and the observer’s latitude.
The observer’s latitude tells the angle from the equator to the observer. If we draw the Earth flat on
and label the declinations above it, the following picture results. North is toward the top. South is
o
toward the bottom. The Declination values start at +90 at the northernmost point and progress
o
lower and lower until they reach -90 .
Chapter 3
How Earth and Sky Work -The Effect of Latitude
4
35
The Latitudes on the Earth and the Declinations on the Celestial Sphere line up, so
Latitude =Declination at Zenith
o
The observer always stands perpendicular (at a 90 angle) to his/her horizon. The part of the
Celestial Sphere on the side of the horizon with the observer’s head can be seen. The rest is
blocked by the horizon and invisible. In this picture, North is up and South down on the paper.
o
The declinations where the horizon cuts the Celestial Sphere, are 90 away from the observer’s
zenith. To find the declinations at the ends, count off the 90 degrees from the horizon. This isn’t the
o
o
o
same as adding or subtracting 90 , since the Declination system goes only from +90 to –90 . The
declination values where the horizon cuts the Celestial Sphere are equal values, but opposite
signs. So
Declination at ends of Horizon = ±( 90-|latitude|)
Either you know the observer’s latitude and can find the horizon, or you know something about the
o
horizon so you can draw the horizon and can draw the observer 90 away.
There are standard questions that you can answer when the observer’s latitude is known. These
questions follow. The blank would have a number in it.
What is the furthest north that an observer at latitude _______ can see?
What is the furthest south that an observer at latitude _______can see?
What is the range of declinations that an observer at latitude ________can see?
What is the range of declinations that an observer at latitude ________ can NEVER see?
What is the range of circumpolar declinations for an observer at latitude ____?
What are these questions asking and how can they be answered?
Circumpolar, the part of the sky that is always above the horizon from your location- The
o
o
circumpolar region starts at either +90 or -90 , whichever is above the horizon for the observer.
The circumpolar region extends to the closest end of the horizon. The circumpolar region NEVER
crosses the equator. The observer’s latitude and the boundaries of the circumpolar region all have
o
o
o
the same sign. Example. For an observer at +60 , the circumpolar region is +30 to +90 . If
Chapter 3
How Earth and Sky Work -The Effect of Latitude
5
36
declination is within the circumpolar region for an observer, EVERY location with that declination
number is circumpolar.
o
o
Never seen-that is, never comes above the horizon Starts either -90 or +90 , whichever is not
visible to the observer. It extends to the closest end of the horizon, the one with sign opposite the
observer’s latitude. It is just the opposite of the circumpolar region (that is the declination values
o
are -1 times the values for the circumpolar region). For the observer at 60 , the never seen region
o
o
would be -30 to -90 .
o
Rise and Set-Between (90 -|latitude|) and -(90
circumpolar and never seen regions are excluded.
o
- |latitude |) This is what remains when the
o
Furthest North Seen – If the observer is in the northern hemisphere, +90 ,
o
If the observer is in the southern hemisphere (90 -|latitude|)
o
Furthest South Seen - If the observer is in the northern hemisphere, -90 +latitude
o
If the observer is in the southern hemisphere -90 .
Range of Declinations Which Can be Seen or Range of Declinations Visible - This is the
summation of declinations that are Always Seen plus the declinations that are Sometimes Seen
o
o
If the observer is in the northern hemisphere, +90 to – (90 -latitude)
o
o
If the observer is in the southern hemisphere -90 to (90 -|latitude|)
o
o
The observer in the previous figure is at latitude 60 , so her zenith is at declination 60 . Her
o
o
horizon is at 90 from the zenith at declinations ± 30 . So what is the
o
o
Furthest north that an observer at latitude ____60 _ can see? +90
o
o
Furthest south that an observer at latitude ___60 _ _can see? -30
o
o
o
Range of declinations that an observer at latitude ___60 _can see? From +90 to -30
o
o
o
Range of declinations that an observer at latitude ___60 _can NEVER see? From -30 to +90
o
o
o
Range of circumpolar declinations for an observer at latitude___60 _? From +90 to +30
To determine whether a body can be seen some, none, or all the time, compare the declination
to the limits of the circumpolar, never seen, and rise and set regions. Or use the diagram as
follows. You will be drawing something like the letter Z.
Chapter 3
How Earth and Sky Work -The Effect of Latitude
6
37
A. Draw the horizon. It goes though the center of the picture and through ±(90 - |latitude| ) The
o
horizon is always at 90 , a right angle, to the observer’s body. It does NOT matter whether
o
observer and the horizon are on the right or left of the picture so long as they are at 90 to one
another.
B. Draw horizontal lines from the points where the horizon touches the Celestial Sphere to the
Celestial Sphere on the other side of the picture. The declination is the SAME number at each end
of the line. Your lines and the horizon make the shape Z or a reversed Z (NOT a sideward Z).
These lines are the boundaries of the circumpolar and never seen regions.
C. Draw a horizontal line representing the daily apparent motion of the body the declination
D. Check whether the path of the star crosses the Z you drew before. If so, it rises and sets. If the
path does not cross the Z and is always above the horizon as seen by the observer, it is
circumpolar. If the path does not cross the Z and is never above the horizon as seen by the
observer, it is Never Seen.
Lost at Sea- Finding Where You Are From What You Can See
In the problems we have been considering, there is only one free parameter, the observer's
latitude. If we know the latitude, then we know the horizon and what can be seen, the circumpolar
region etc. There is little variety.
On the other hand, an observer can find his latitude by noting the range of circumpolar bodies,
the furthest south or north that can be seen etc. It is just a matter of using the information to find
o
the horizon, then finding the location of the observer (90 from the horizon)
Example: You notice Vega at your Zenith, what is your latitude? Vega is a star and you can
find its declination from a star map.
Answer: You know that Latitude of observer = Declination of zenith and the problem says that
Vega, is at the zenith. So
o
Vega’s declination = declination at the observer’s zenith=observer’s latitude =39
Example: If you can
see as far north as
o
20 , what is your
latitude?
Answer:The words
imply that the horizon
o
goes through 20 . It
also goes through
the center of the
o
Earth and -20 . So
draw the horizon.
Draw the observer
perpendicular to the
horizon on the side
such that he can see
o
o
20 and south of 20 ,
but NOT see north of
o
20 . If you are unsure
o
o
of which observer, draw both (the one at 20 and the one at -20 ) and check which one can NOT
o
see further north than 20 . The latitude of the observer equals the declination at the observer's
zenith. How do you know whether the observer is in the North or the South? Be sure that your
o
o
observer cannot see further north than 20 Ans –70
Chapter 3
How Earth and Sky Work -The Effect of Latitude
7
38
Example: You notice that Vega is circumpolar, but
nothing further south is. What is your latitude?
Look up Vega’s declination on a star map. If Vega
is circumpolar, its entire path is above the horizon.
Since nothing further south than Vega is
circumpolar, the horizon must touch Vega’s path on
one side. It doesn’t matter which side.
So draw the horizon though Vega’s declination, the
center of the Earth, and the negative of Vega’s
declination.
The observer will be perpendicular to the horizon. In
this case, the observer will be in the northern
hemisphere, since Vega is.
When you draw the line representing Vega’s motion,
you can simply draw the observer such that the
entire path is above the horizon.
The Sky as We See It We have been making diagrams as though we are outside the
Celestial Sphere. But how does the path of a star really look from the ground?
The figure below shows how celestial objects appear to move through the sky. It is drawn for a mid
northern latitude location. Circumpolar objects appear to circle the pole, always remaining above
the horizon. Objects that rise and set make arcs starting in the East and ending in the West. The
never seen objects are, of course, never seen. The filled ellipse represents the ground.
As time goes by, the position of each object normally changes compared to the horizon and to the
cardinal points (the N, E, S, W positions on the horizon).
The only points that don’t appear to move are the North Celestial and the South Celestial poles.
The North star, Polaris, is about 5/6 of a degree from the North Celestial Pole, changes its position
a little. There is no bright star near the South Celestial Pole.
Altitude/Azimuth System
Chapter 3
How Earth and Sky Work -The Effect of Latitude
8
39
Right Ascension and Declination are useful because they tell the position of a location on a star
map. They don’t correspond to a fixed direction compared to the observer’s horizon and meridian.
The Altitude and Azimuth system does.
o
o
Altitude is the angle from body to horizon. Altitude is 90 at the zenith, 0 at the horizon. Negative
altitudes are sometimes used to describe positions below the horizon (invisible).
Azimuth is the angle from
north to the point on the
horizon below the object.
o
Azimuth runs from 0 at the
North
Cardinal
Point,
o
through 90 eastward and
o
180 to the south.
Altitude
and
Azimuth
change as the objects rise
and set. So there are no
books of Altitude and
Azimuth coordinates. But
these coordinates are very
useful for pointing out
objects in the sky to nearby
people. They are also used
by some telescopes. But
these telescopes use a
computer and a clock to
figure out where the object
is as it moves across the sky.
Altitude of the Celestial Pole
The altitude of the celestial pole, whichever one you can see, is equal to the latitude of the
observer. Since the star Polaris is nearly at the North Celestial Pole, the altitude of Polaris equals
the
observer’s
latitude.
This
makes
it
easy
to
find
latitude.
Chapter 3
How Earth and Sky Work -The Effect of Latitude
9
40
Measure
o
From
Pole
North Celestial
Pole
location of
Polaris
o
Declination
14 place AWAY
then
the
horizon
90
9 o -14 o =7 o
0
6
Find the Declination at the
Zenith
which Equals Observer's
Latitude
Observer is perpendicular to
horizon
a
t9 o -76o =1 o
Horizon
North
Celestia
lPol
e
0
4 o -altitude of
o -(90
or
90
altitude
of pole)=
pole
South Celestial
Pole
Altitude of Polaris Equals the Observer’s Latitude
o
Ex. Polaris’ altitude is 14 . Where are you?
o
Ans. Latitude 14 .
o
Example Polaris is at altitude 83 . What is your latitude?
Orientation Practice Problems Set I (you may look up declinations etc. on the star map)
o
1) What is the range of declinations that can be seen from latitude 20 ?
o
2) What is the range of declinations, which is circumpolar from latitude 20 ?
o
3) What is the furthest north that can be seen from latitude -43 ?
o
4) What is the furthest south that an observer at latitude at latitude -63 can see?
o
5) If you are at latitude 32 , what is the range of declinations that are circumpolar ?
o
6) When the altitude of the North Celestial Pole is 14 , where are you?
o
7) If you are at latitude -30 , what is the altitude of the SCP? of the NCP?
Chapter 3
How Earth and Sky Work -The Effect of Latitude
10
41
8) What is the furthest south latitude you can be so that the star Vega will be circumpolar for you?
o
9) What is the range of declinations that are visible from -60 ?
10) Regulus is circumpolar. It just grazes the horizon at its lowest point, what is your latitude?
11) You are lost at sea. Antares just comes above the horizon at culmination(its highest point),
What is your latitude?
12) If you notice that Betelgeuse is circumpolar, but nothing further south is, what is your latitude?
13) If Deneb just rises and nothing further north is visible, what is your latitude?
14) When Antares is circumpolar and nothing further north is, what is your latitude?
15) What latitude allows the observer to see the largest variety of celestial objects?
o
o
o
o
o
o
o
o
o
o
Answers 1) from 90 to -70 2) +70 to +90 3) +47 4) -90 5) 58 to 90 6) +14 7) SCP 30
o
o
o
o
altitude, NCP -30 altitude, below the horizon 8) Vega at 36 , latitude of observer 54 9) +30
o
o
o
o
o
to -90 10) Regulus at +12 , observer +78 11) Antares at -26.5 , observer at 63.5 12)
o
o
o
o
o
Betelgeuse at 7 , observer at 83 13) Deneb at 45 you at -45 14) Antares at -26.5 , observer
o
o
at -63.5 15) The equator, latitude 0
Chapter 3
How Earth and Sky Work -The Effect of Latitude
11
42
Chapter 4 How Earth and Sky Work -The Effect of Time
We have learned what can be seen from various latitudes, provided you wait long enough. How
long, is long enough? Half a sidereal day would be long enough, if sunlight were no problem After
half a spin, the part of the sky that is seen changes as much as it ever will. There is NO difference
in what can be seen over the course of the year (although there is a difference in which objects are
up during the day). Solar and Sidereal Time tell the position of the observer compared to the Sun
and stars respectively. They allow us to assess what can be seen at any time and date.
Solar Time tells the angle of the Observer’s meridian with respect to the Sun.
Noon is when the Sun is on the observer’s meridian (on the side that can be seen)
Midnight is when the Sun is on the meridian when it is the highest. The observer points away from
the Sun.
PM, meaning “post meridiem”
observer’s meridian.
equals the number of hours since the Sun has been on the
AM, meaning “ante meridiem” means before the Sun is on the meridian. It equals the number of
hours since midnight.
The pictures we will use are as seen from above the Earth’s north pole. Earth spins and orbits
counterclockwise in this view.
In the picture below, the circle represents the observer’s meridian. Find the observers’ solar times.
Draw another observer on the figure above. Make it an observer for whom it is midnight.
Chapter 4
How Earth and Sky Work -The Effects of Time
1
43
The Effect of Date and the Earth’s Orbit
The stars are located far far outside the Solar System. So Earth’s motion is tiny compared to the
distance to the stars. We will identify star positions by their Right Ascensions.
The Earth orbits the Sun once per year, returning back to the same position in orbit more or less.
The following diagram is your reference for combining the position with the position of the stars. Be
st
rd
sure to fill it in. The circles are positions of the Earth every 21 of the month (23 of September).
The lines tell the Right Ascension of the stars in that direction. There are 24 total hours.
The date tells the Earth’s position in orbit, which in turn determines the right ascension (and
sidereal time) at midnight. Conversely, if we knew the sidereal time at midnight, it would be easy to
find the date. The solar and sidereal times take every value every day.
There are only two motions, so only two different things can be specified. The Earth spins and
orbits, and these two motions determine the date, the solar time and the sidereal time.
Solar Time tells the position of the observer's meridian compared to the Sun.
Date -Tells the position of the Earth in its orbit.
Sidereal Time equals the Right Ascension on the observer's meridian (definition)
Although all sidereal times and all solar times occur every day, the sidereal time corresponding to a
given solar time depends on the date. On September 23, at midnight, Right Ascension 0 hr is on
the meridian.
Chapter 4
How Earth and Sky Work -The Effects of Time
2
44
As time progresses both solar and sidereal time increase at almost the same rate. Every day both
solar and sidereal time go through all 24 hours. Sidereal hours are a little smaller than solar hours,
so 24 sidereal hours are completed in 23 hr
56min of solar time.
Because the Earth orbits the Sun, the midnight
direction changes, so the sidereal time at
midnight changes. It is easy to find the
sidereal time at midnight by remembering how
the diagram above works. Memorize that
midnight on September 23 is 0 hr sidereal time
and that:
The Sidereal Time at midnight,
increases
2 hours per month
1/2 hour per week
4 minutes per day
Orientation Practice Problems Set II
What is the Solar Time in the figure below for each observer?
3) Draw a picture with an observer who is at 6 AM
4) Draw a picture with an observer who is at 5 PM
5) Draw a picture with the Earth on Oct 21. Include the Sun, and the Right Ascension markers.
6) Draw a picture with the Earth on Aug 8, Include the Sun, and the Right Ascension markers.
Solar Time, Sidereal Time and Date Given any two items from among Solar Time,
Sidereal Time and Date, the third can be found. This is
because there are only two motions; Earth spinning
and Earth orbiting.
The date tells where to position the Earth and the time
(solar or sidereal, whichever time you have) to
determine the observer’s position. From the drawing, it
is possible to find the other time.
Example: What is the sidereal time at 6 AM on May
21?
The picture follows. The answer is 22 hr, but why?
The observer’s meridian points along the same
direction as her body. The stars in that same direction
are very far away, so it is important NOT to consider
the printed numbers on the picture, but to think of the
direction parallel to the body line starting from the Sun,
as is shown below.
To 22 hr,
parallel
to the
observer
One way to find sidereal time for an observer is to
Chapter 4
How Earth and Sky Work -The Effects of Time
3
45
estimate the direction of an arrow at the Sun, but parallel to the observer’s body.
A better way to find the correct time is to use midnight as a reference and to count the number of
hours from midnight to get to the desired time. This method ensures that the result is independent
of imperfections in drawing the figure. Since sidereal hours and solar hours are nearly the same
length, an accurate answer will result.
In the example given, the solar time was 6 AM, six
hours after midnight. The sidereal time at midnight
was 16 hr, based on the date May 21. So 6 hr
LATER than 16 hr is 16+6=22 hr. You get the
same answer, but there is less \dependence on
the drawing.
Example: What is the sidereal time at 9 PM on
Aug 21?
The sidereal time at midnight is 22 hr and you
could subtract three hours to get to 9PM. So 22
hr– 3 hr = 19 hr. The drawing shows the same
thing. Here it feels natural to subtract 3 hours to
go from midnight to 9pm (3 hours earlier). It is
equally correct to add 21 hours going forward from
midnight to 9PM.
Adding the hours
gives22hr+21hr=43hr hours. Since there is no
sidereal time of 43hr, the remedy is to realize that
24 hr is the same as 0 hours. Subtracting 43hr-24
hr=19hr.
18
6/2
hr
1
Eart
h
0
9/2
hr
3
To 19 hr,
parallel
to the
observer
12
3/2
hr
1
6
12/2
hr
1
We have been counting hours away from midnight to get one kind of time if we know the other.
Organize the Computation Using a Table Pretend there are two people involved. One is
Midnight Man, for whom it is always midnight. The other is the protagonist, the one the problem
is about. ALL of the data is about the
protagonist, ALWAYS. The date is the same
for the protagonist and the Midnight Man, so
there is only one row for the date. The row
and column headings tell what to enter.
Make two correct addition problems going
DOWN. One is in the Solar Time column
and the other in the Sidereal Time column.
Read down the column to add the first two
values and find the third. In each column
Midnight Man’s time+ Hours to Add =
Protagonist’s time.
Problems are always read the same (going
down) when complete, but the order in
which they get filled in varies. The arrows
indicate that data are related. In the case
of the hours to add, the values are identical.
In the case of date and midnight sidereal
time, one determines the other.
The original motivation for making this table
was to make it easier to find the DATE when
the solar and sidereal times are known. It
always works provided that no errors are made. However, it has no checks to indicate whether an
error has occurred. Sketching the picture is useful for a check. If the table and picture disagree,
there is some error.
Chapter 4
How Earth and Sky Work -The Effects of Time
4
46
Example: If it is 4 AM on November 21, what is the sidereal time? Ans. Fill in the block in the
Solar Time/Protagonist block with 4AM, the solar time for the Protagonist. Fill in the Date block with
the date, 11/21.
Solar Time
Midnight
Man
Hours
Add
Date
Midnight
same
to
Protagonist
Midnight
Man
Hours
Add
Sidereal
Time
4AM
Solar Time
Sidereal
Time
Midnight
4hr
Date
The same amount of time, 4 hr,
is added to the Sidereal Time at
Midnight.
same
to
+4 hr
Protagonist
11/21
Use your knowledge of the
Sidereal Time at Midnight on
November 21 to fill in 4 hr for
Midnight Man’s Sidereal Time.
Use
your
knowledge
of
arithmetic to fill in 4hr to add to
Midnight Solar Time to get to 4
AM.
+4 hr
11/21
4AM
Now add the 4hr to Midnight Man’s Sidereal Time at Midnight to
get the Protagonist’s Sidereal Time.
Solar Time
Sidereal
Date
Time
Midnight
Man
Hours
Add
Midnight
same
to
Protagonist
4hr
+4
+4
4AM
8hr
11/21
So the answer is that the protagonist’s sidereal time is 8 hr, but draw the picture to check.
Example: Find the solar time at 6hr on April 21? You could draw it, or use the table
So enter the protagonist’s
Solar Time
Sidereal
Date
Sidereal Time (6 hr) and the
Time
Date. You know that 6hr is a
Midnight
Midnight
sidereal time, because it doesn’t
Man
say AM or Pm or noon or
midnight.
Hours
to
same
4/21
Add
Protagonist
Chapter 4
6 hr
How Earth and Sky Work -The Effects of Time
5
47
Use your knowledge of sidereal time to fill in 14 hr for the sidereal time at midnight on 4/21.
Midnight
Man
Hours
Add
Solar Time
Sidereal
Time
Midnight
14hr
same
to
Date
4/21
6 hr
Protagonist
And use your knowledge of arithmetic to to subtract 8 hr from the sidereal time at midnight to get to
the protagonist’s sidereal time of 6 hr.
Midnight
Man
Hours
Add
Solar Time
Sidereal
Time
Midnight
14hr
same
to
-8 hr
-8 hr
Date
4/21
6 hr
Protagonist
Subtract the same 8 hr from Midnight to get to the Protagonist’s Solar Time, 4 PM.
Midnight
Man
Hours
Add
Solar Time
Sidereal
Time
Midnight
14hr
same
to
Protagonist
-8 hr
-8 hr
4PM
6 hr
Date
4/21
Example: What is the date when Betelgeuse is on the meridian at 7 PM? It is not easy to draw
this, because the position of the Earth is not known. On the other hand, the solar time (7 PM) is
known and the sidereal time is known because you can look up the Right Ascension of Betelgeuse
(6 hr) and since Betelgeuse is on the meridian, the sidereal time is 6 hr. So using the table
Solar Time
Sidereal
Date
Time
Midnight
Man
Hours
Add
Midnight
same
to
Protagonist
7 PM
6 hr
Now complete the arithmetic problem in the Solar Time column. So, reading down Midnight plus
what gets you to 7 PM? The number of hours to add is -5. So fill the –5 hours into the solar time
column and the sidereal time column.
Chapter 4
How Earth and Sky Work -The Effects of Time
6
48
Solar Time
Midnight
Man
Hours
Add
Sidereal
Time
Date
Midnight
same
to
Protagonist
- 5 hr
- 5 hr
7 PM
6 hr
Now complete the arithmetic problem for the Sidereal Time. What minus 5 gives 6? Eleven, of
course. It is very common to make an error in this arithmetic. Try writing the number down in the
top row. Then read aloud to yourself and see whether it sounds right. 11-6=6. OK
Solar Time
Sidereal
Date
Time
Midnight
Man
Hours
Add
Midnight
same
to
Protagonist
11 hr
- 5 hr
- 5 hr
7 PM
6 hr
So what is the date when it is 11 hr Sidereal Time at midnight? Eleven hours is half way between
10 hours and 12 hours, so the position of the Earth along its orbit is half way between Feb 21 and
Mar 21. We approximate each month as 30 days. So half way between Feb 21 and Mar 21 is 15
st
th
days before the 21 or the 6 of March. (Ignore the 28 days or 31 day months.
Solar Time
Sidereal
Date
Time
Midnight
Man
Hours
Add
Midnight
same
to
Protagonist
11 hr
- 5 hr
- 5 hr
7 PM
6 hr
Mar 6
Now draw Mar 6 and one of the times. See whether the other time is consistent with the picture. If
not, there has been some computational error.
Orientation Practice Problems Set III
1) On April 7, what is the sidereal time at 11 PM?
2) On Aug. 21, what is the sidereal time at 9 AM?
3) If Orion is on the meridian, what is the sidereal time?
4) What time would you observe Gemini on the meridian on October 21?
5) If it is 13 hours on May 21, what is the solar time?
6) If it is July 4, and it is 10 PM, what is the sidereal time?
7) If you see Taurus, at 4 hours Right Ascension on the meridian and it is Feb. 21, what is the
sidereal time? What is the solar time?
8) If it is 4 hr sidereal time and 12 noon, what is the date?
9) When you see Libra on the meridian at 3 AM, what is the date?
10) What is the Right Ascension of the Sun on Nov.7?
Answers Set II Get within an hour or so. Be sure to get the AM and PM correct. 1) a 3 AM b 10 PM
c 11:30 AM 2) a 7 AM b 10 AM c 2PM
Chapter 4
How Earth and Sky Work -The Effects of Time
7
49
The direction of the
Earth with respect to
the Sun doesn’t
matter for the answer.
There is no solar or sidereal time specified, so there is no
protagonist to draw
7) About 10 AM
Set III 1) 12 hr 2) 7 hr 3) 6 hr approx. 4) 5AM 5) 9
PM 6)17 hr 7) 4 hr, 6 PM 8) May 21 9) Libra is at about
15 hr, you can look this up on a map, so the sidereal time is
15 hr, the date is Mar 21 10) 15 hr
Putting Latitude and Time Together
As we consider what can be seen at any time, it is
necessary to know the sidereal time, and the latitude. We
have been computing the sidereal time and the range of declinations visible separately. To
combine the two, use the horizon plot provided.
This curve is meant to be overlaid on the mercator projection map of the entire sky. The heavy
curve is the horizon. The values of marked near the curves distinguish the view from different
o
latitudes. Diablo Valley College is at about +38 . The rectangular grid on the page is the right
ascension and declination grid; the same as on the map. The vertical line is the meridian.
To use the curve for the Northern Hemisphere, match the bottom boundaries (not the edge of the
paper, but the straight line at the bottom) of the map and the sheet with the curves. Match the
meridian with the value of Right Ascension =Sidereal Time. Everything above the curve will be
visible. Usually the curve will hang off to either the right or left edge and will leave the other side
uncovered. To find the horizon on the uncovered side, remember that the map is supposed to be
the surface of a sphere, so the right and left edges (Right Ascension 0 hr) really should be
connected. The part of the horizon overlay which is hanging off will be on top of the rest of the
map, where it is needed.
Using the Visibility Curve
We have been considering the effect of latitude separate from the effect of time. If you want to
know exactly what can be seen, at any particular time, it is a little more complex. The curves on the
next page are designed to be used to block the parts of the sky, on the mercator project, that you
cannot. see at a given moment.
Each curve is labeled with the latitude for which it applies. It is easiest to copy the page and cut
along the line for your latitude with a scissor. This embodies the effect of your latitude. Be careful to
follow the curve accurately, they cross.
Compute the Sidereal Time for whenever you want to observe. Align the meridian on the visibility
curve up on the Right Ascension equal to the Sidereal Time .
Line up the edge of the grids on the mercator star map and the bottom of the visibility curve. For
o
observing in the Northern Hemisphere, line up the bottom of the visibility curve grid with the –90
line on the star map. For observing in the Southern Hemisphere, turn the sheet with the visibility
o
curve upside down and line up the bottom of the curve with the +90 line on the map.
Chapter 4
How Earth and Sky Work -The Effects of Time
8
50
Chapter 5 Positions of the Sun and Moon
Objects in our Solar System appear to move over the course of weeks to months because they
are so close. This motion caused ancient astronomers to use the name “planets”, which means
“wanderers” for the planets that they could see. Comets show tails and so were named
differently. Asteroids, moons and planets past Saturn are too faint to see without telescopes, so
they were unknown.
Since Solar System objects move, we do not memorize their positions the way that we can for
stars.. But we can understand how they move and specify their Right Ascensions and
Declinations.
The Solar Motion
As we look from the Earth toward the Sun, it appears to be in front of the stars on the opposite
side of our orbit. As the Earth orbits the Sun, this direction changes and the Sun appears to
move in front of each of the constellations of the zodiac. The figure shows the view from above
the Earth’s North Pole.
The Sun’s Right Ascension is the Right Ascension BEHIND theSun as we look straight
across our orbit. This
direction is the same as
the direction of the
meridian
at
noon.
Another way to look at it
is that the Sun’s Right
Ascension is always 12
hours different from the
sidereal time at midnight.
The Babylonians started
to specify the Sun’s
position
using
this
concept.
Each year the Sun
appears to move all the
way
through
the
constellations,
at
an
average rate of a little
less than 1 degree each
day. This small motion is
not very noticeable as
you watch the sky. It is a
much smaller effect than
the rising and setting of
the entire sky due to the
Earth’s rotation.
The star map that follows shows the Sun’s path among the stars, the ecliptic. The Sun’s path is
called the ecliptic, because eclipses of the Sun and/or Moon occur when the Moon is nearly on
the ecliptic. The rest of the planets and the asteroids are usually found near the ecliptic because
the solar system is nearly a plane (flat).
On the star map, the ecliptic is a wavy line. It goes north and south of the celestial equator due to
the tilt of the Earth’s axis. It is defined as the path of the Sun, so the Sun is ALWAYS on the
ecliptic, NEVER anywhere else. If we know the Right Ascension of the Sun, from the date, we
can find the point on the ecliptic with that Right Ascension, and read off the declination, at least
approximately. Knowing the date. we can find the Sun's Right Ascension.
Chapter 5
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Motions of the Sun and the Moon
1
51
For example, if we know it is Feb 21, then the Right Ascension behind the Sun is approximately
22 hr. Earth has 10 hr at midnight,, so 22 hours is directly across from the Earth, behind the Sun.
o
The declination ON the ecliptic, at 22 hours is about -12 . This can be found by reading directly
off the ecliptic curve.
One way to remember the declination of the Sun is to remember the overall shape of the ecliptic
o
curve and that the Sun is at 0h and 0 on March 21, the traditional starting point of the year. The
Sun is at positive declinations (in the northern hemisphere) from March 21 through September
23, the traditional summer months. It is at a southern declination during the rest of the year, the
winter months.
Check yourself: What is the Right Ascension and Declination of the Sun on Aug 21?
To find the declination of the Sun on any day, it is necessary to remember the form of the
ecliptic curve. Once the date is known, the Right Ascension of the Sun follows. Once the Right
Ascension is known, there is only one point on the ecliptic for the Sun to be. Estimate the
declination ON the ecliptic given the Right Ascension
Seasons
As you have doubtless noticed, it is colder and there are fewer hours of daylight (out of each 24)
during the winter. The reason for this lies in the tilt of the Earth’s axis.
o
The Earth’s rotation axis is tilted about 23.5 compared to the direction perpendicular to its orbit.
The axis keeps the same direction over the year, so sometimes one pole is tipped toward the
Sun, and other times the other pole is. The distance to the Sun changes only slightly over the
year, but the length of the daylight and the intensity of the light can change dramatically. The
following figure shows how the tilted axis changes where the day/night line falls. On December
21, the entire north polar area is in shadow and the south pole area is in sunlight. On June 21, the
situation is reversed.
The area that the sunlight spreads over is larger on the part of the Earth is tilted away from the
Sun, smaller when pointed toward So the hemisphere pointed away from the Sun gets fewer
Chapter 5
Astronomy 110
Motions of the Sun and the Moon
2
52
hours of daylight and the light it does get is spread out more and is less intense than average.
The hemisphere gets colder and colder until the Earth's motion on its orbit changes the situation.
What about the effect of distance to the Sun? The earth’s orbit is not exactly a circle. The
distance varies by ±1.67%, with the closest point on the orbit occurring on Jan 6. This small
distance change does not matter very much. It might seem that the southern hemisphere should
have hotter summers and colder winters because the distance change accentuates its summer
and winter. Actually, the land in the southern hemisphere is near the equator and there is a great
deal of water. So the climate in the southern hemisphere is pretty mild.
Other planets, notably Mercury, Mars and Pluto, have orbits with substantial eccentricity. So their
distances from the Sun vary considerably and the amount of light they get does too.
Precession
Actually, the direction that our axis points is NOT always the same. It rotates slowly with a period
of 25,800 years, The motion of
the earth is shown in the figure.
The direction of Earth’s poles
changes, but the stars do not.
There is no “start date” or “end
date” for the precession motion.
It just continues.
The polar star maps in chapter
2 show the path of the poles.
When the Egyptian pyramids
were built, the north star was
the star Thuban, the brightest
star in the constellation Draco
(not very bright). The star Vega
will be near the North Celestial
Pole, the point above the
Earth’s North Pole in about half
a cycle from now (about 13,000
years).
There has been a conscious
o
decision to maintain the Declination system with the ±90 positions lined up with the poles of the
Earth. The zero point of Right Ascension is the Sun’s position on the Vernal Equinox (when the
apparent position of the Sun moves north of the Celestial Equator). As the Earth’s axis changes
Chapter 5
Astronomy 110
Motions of the Sun and the Moon
3
53
direction, the coordinates of every object change. When accurate positions are published, they
are given with the word “Epoch___”. That is the Epoch tells what date the positions were for.
It may seem that
the
changes
introduced
by
precession
are
too
small to
matter. But the
overall motion in
declination is up
o
to 47 and the
Right Ascensions
change through
the entire range
of 24 hours. As
the coordinates of an object change, whether it is always, sometimes or never visible from a
location change.
Precession changes correspondence between the position of the Earth in its orbit and the
season. In the following picture, the constellation names show where the stars are with respect
to the orbit.
What should the date be at the position labeled? There may be no one right answer, but the
convention that we now are living by is that the date will be MARCH 21. Why? Because it is the
Vernal Equinox, the time when spring starts, the time when the Sun goes north of the Celestial
Equator.
A way to see this is to look at the Earth and the daylight parts. Currently, summer in the Northern
Hemisphere occurs when the Earth is on the left, where the North Pole gets 24 hours of daylight.
In 12,900 years, the position of the Earth where the North Pole has 24 hours of daylight, will be
on the right of the picture. We have chosen to keep the dates in the year aligned with the
seasons. So summer in the north will remain in June. This is called the Tropical Year There is no
way to keep the dates and the seasons aligned and also keep the position of the earth in its orbit
aligned with the dates.
The Tropical Year, has leap year days (Feb 29) at the proper interval to keep the seasons and
the dates aligned. It has 365.242 days in a year. (To keep the same part of the orbit aligned with
the same date we’d use the sidereal year, 365.2564 days.).
This combination of precession and the tropical year means that the Gemini and Taurus, which
are seen near midnight in December will be seen near midnight in June in the future. You may
have noticed that correlation of constellation and date from your horoscope are different from the
Chapter 5
Astronomy 110
Motions of the Sun and the Moon
4
54
constellation behind the Sun on that same date. This is because the astrologers decided not to
update the constellation correlation due to precession. The dates they use are from around the
time of the Greeks (~2300 years ago).
So what is your “real” sign?
The Lunar Story The Moon orbits the Earth and moves around the Sun together with the Earth.
Earth
revolves around the Sun (orbits) once per____________
Earth rotates on its axis once per ______________
Moon orbits the Earth once per ________________
Time between first quarter and full moon _________
Phases of the Moon depend on the angle to the Sun. In the following picture, color the moon to
show the bright and dark parts based on illumination from the Sun. Then draw the appearance of
the Moon as seen from the Earth and name each phase (each shape/position in orbit
combination).
Chapter 5
Astronomy 110
Motions of the Sun and the Moon
5
55
The Moon’s Right Ascension, that is, the Right Ascension of the part of the sky behind the
Moon, can be found from the day of the year and the phase of the Moon. The Moon's phase tells
the Solar time when the Moon is on the meridian. Pretend the protagonist has that Solar Time.
Then use the date and the Solar Time, to find the Sidereal Time when the Moon, with its Right
Ascension, is on the Meridian. Then Sidereal Time = Moon's Right Ascension.
Use the lunar phase to create a protagonist who has the Moon on the observer’s meridian.
Then use the table to find the protagonist’s sidereal time. This is the same value as the
Moon’s Right Ascension.
Chapter 5
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Motions of the Sun and the Moon
6
56
How often do Eclipses
The
inclination of the Moon's orbit, approximately
occur?
5 degrees, keeps the shadows of both Earth and Moon
from causing eclipses unless the three bodies are nearly
in a straight line. Most of the time the tilt of the moon's
orbit keeps the Moon above or below the Earth-Sun line.
Su
n
For an eclipse to occur, the line of nodes of the Moon’s orbit must be nearly along the direction
toward and away from the Sun. (Nodes are the points where the Moon’s orbit and the Earth’s
orbit cross and the line of nodes joins the two intersections. )
When the nodes are properly aligned, a Lunar and a Solar eclipse always occur, one at new
moon, the other at full moon, about two weeks apart. Sometimes the alignment of the line of
nodes is just right and three eclipses occur over one lunar month.
Chapter 5
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Motions of the Sun and the Moon
7
57
Once the two or three eclipses have occurred, the “eclipse season” is over. There cannot be any
more eclipses until the line of nodes again points toward the Sun, nearly six months later.
If the Moon’s orbit did not change, the situation would be like the drawing immediately below.
Can there be Eclipses Here?
Can there be Eclipses
Here?
But, the tilt of the Moon’s orbit changes both direction and angle. The direction of the tilt makes a
complete rotation every 18.61 years due to the gravity from the Sun and the other planets. As the
direction changes, the line of nodes regresses, i.e. it goes retrograde and the alignment of the
nodes for another eclipse season occurs less that 6 months after the previous one. The diagram
below depicts the how the direction changes.
The tilt of the orbit varies from about 9 minutes (0.15 degrees) on a 173 day cycle.
Orientation Practice Problems Set IV
1) At what time is the first quarter Moon on the meridian?
2) If you can see a crescent moon and it is 5 AM, is it a waxing or a waning moon?
3) You want to fish in the darkness (so the fish won’t see your boat, but you want to launch the
boat in moonlight (so that you can see what you are doing), but after sunset. You will fish from
3AM until after dawn and you do not want to sit in the boat starting from sunset.
4) If it is full moon on Oct. 15, when is the new moon?
5) If there is a third quarter moon on April 1, when will waning crescent be?
6) If it is March 21, what is the Right Ascension of the third quarter moon?
7) If it is Oct. 7, what is the Right Ascension of the waxing gibbous moon?
8) If you see the waning crescent moon at 15 hr Right Ascension, what is the date?
9) When the waxing crescent moon is in Taurus, at 4 hr, what is the date?
10) What is the Right Ascension of the third quarter moon on May 7?
11) If there is a lunar eclipse on March 12, when can there be a solar eclipse?
12) What is the Right Ascension and declination of the Sun on Jan21?
Answers
o
Solar position on Aug 22 the Right Ascension is about 10 hr and the declination is about +12
Answers Set IV
1) 6 PM 2) Waning 3) You want the moon to set at 3 AM, so it must be Waxing Gibbous. 4) Oct.
29 5) April 5 6) 18 hr 7) 22 hr 8) Treat it as though the protagonist were at 9 AM, so midnight is 9
hr earlier or at 6 hr, which makes it Dec. 21. 9) April 7 10) 21 hr 11) Either 2 weeks before, two
O
weeks after, or 5 and one half lunar months later (or earlier) 12) 20 hr and -20
Chapter 5
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58
Solar Eclipses 2005-2030
Date
Eclipse Saros
Type
2005 Apr 08 Hybrid 129
Eclipse Predictions by Fred Espenak,NASA/GSFC
Eclipse
Central Geographic Region of Eclipse Visibility
Magnitude Duration
1.007
00m42s N. Zealand, N. & S. America [Hybrid: s Pacific,
Panama, Colombia, Venezuela]
0.958
04m32s Europe, Africa, s Asia
[Annular: Portugal, Spain, Libya, Sudan, Kenya]
1.052
04m07s Africa, Europe, w Asia
[Total: c Africa, Turkey, Russia]
0.935
07m09s S. America, w Africa, Antarctica [Annular:
Guyana, Suriname, F. Guiana, s Atlantic]
0.874
Asia, Alaska
0.749
S. America, Antarctica
0.965
02m12s Antarctica, e Australia, N. Zealand
[Annular: Antarctica]
1.039
02m27s ne N. America, Europe, Asia [Total: n Canada,
Greenland, Siberia, Mongolia, China]
0.928
07m54s s Africa, Antarctica, se Asia, Australia
[Annular: s Indian, Sumatra, Borneo]
1.080
06m39s e Asia, Pacific Ocean, Hawaii
[Total: India, Nepal, China, c Pacific]
0.919
11m08s Africa, Asia
[Annular: c Africa, India, Malymar, China]
1.058
05m20s s S. America
[Total: s Pacific, Easter Is., Chile, Argentina]
0.857
Europe, Africa, c Asia
0.601
e Asia, n N. America, Iceland
0.097
s Indian Ocean
0.905
s Africa, Antarctica, Tasmania, N.Z.
0.944
05m46s Asia, Pacific, N. America
[Annular: China, Japan, Pacific, w U.S.]
1.050
04m02s Australia, N.Z., s Pacific, s S. America
[Total: n Australia, s Pacific]
0.954
06m03s Australia, N.Z., c Pacific
[Annular: n Australia, Solomon Is., c Pacific]
1.016
01m40s e Americas, s Europe, Africa
[Hybid: Atlantic, c Africa]
0.984
s Indian, Australia, Antarctica
[Annular: Antarctica]
0.811
n Pacific, N. America
1.045
02m47s Iceland, Europe, n Africa, n Asia
[Total: n Atlantic, Faeroe Is, Svalbard]
0.787
s Africa, s Indian, Antarctica
1.045
04m09s e Asia, Australia, Pacific
[Total: Sumatra, Borneo, Sulawesi, Pacific]
0.974
03m06s Africa, Indian Ocean
[Annular: Atlantic, c Africa, Madagascar, Indian]
0.992
00m44s s S. America, Atlantic, Africa, Antarctica [Annular:
Pacific, Chile, Argentina, Atlantic, Africa]
1.031
02m40s N. America, n S. America
[Total: n Pacific, U.S., s Atlantic]
0.599
Antarctica, s S. America
0.337
s Australia
0.736
n Europe, ne Asia
2005 Oct 03
Annular 134
2006 Mar 29
Total
2006 Sep 22
Annular 144
2007 Mar 19
2007 Sep 11
2008 Feb 07
Partial 149
Partial 154
Annular 121
2008 Aug 01
Total
2009 Jan 26
Annular 131
2009 Jul 22
Total
2010 Jan 15
Annular 141
2010 Jul 11
Total
146
2011 Jan 04
2011 Jun 01
2011 Jul 01
2011 Nov 25
2012 May 20
Partial
Partial
Partial
Partial
Annular
151
118
156
123
128
2012 Nov 13
Total
133
2013 May 10
Annular 138
2013 Nov 03
Hybrid
2014 Apr 29
Annular 148
2014 Oct 23
2015 Mar 20
Partial
Total
153
120
2015 Sep 13
2016 Mar 09
Partial
Total
125
130
2016 Sep 01
Annular 135
2017 Feb 26
Annular 140
2017 Aug 21
Total
145
2018 Feb 15
2018 Jul 13
2018 Aug 11
Partial
Partial
Partial
150
117
155
Chapter 5
Astronomy 110
139
126
136
143
Motions of the Sun and the Moon
9
59
Date
2019 Jan 06
2019 Jul 02
2019 Dec 26
2020 Jun 21
2020 Dec 14
2021 Jun 10
2021 Dec 04
2022 Apr 30
2022 Oct 25
2023 Apr 20
2023 Oct 14
2024 Apr 08
2024 Oct 02
2025 Mar 29
2025 Sep 21
2026 Feb 17
2026 Aug 12
2027 Feb 06
2027 Aug 02
2028 Jan 26
2028 Jul 22
2029 Jan 14
2029 Jun 12
2029 Jul 11
2029 Dec 05
2030 Jun 01
2030 Nov 25
Eclipse Saros Eclipse
Central Geographic Region of Eclipse Visibility
Type
Magnitude Duration
Partial 122 0.715
ne Asia, n Pacific
Total
127 1.046
04m33s s Pacific, S. America
[Total: s Pacific, Chile, Argentina]
Annular 132 0.970
03m39s Asia, Australia
[Annular: Saudi Arabia, India, Sumatra, Borneo]
Annular 137 0.994
00m38s Africa, se Europe, Asia
[Annular: c Africa, s Asia, China, Pacific]
Total
142 1.025
02m10s Pacific, s S. America, Antarctica
[Total: s Pacific, Chile, Argentina, s Atlantic]
Annular 147 0.943
03m51s n N. America, Europe, Asia
[Annular: n Canada, Greenland, Russia]
Total
152 1.037
01m54s Antarctica, S. Africa, s Atlantic [Total: Antarctica]
Partial 119 0.639
se Pacific, s S. America
Partial 124 0.861
Europe, ne Africa, Mid East, w Asia
Hybrid 129 1.013
01m16s se Asia, E. Indies, Australia, Philippines. N.Z.
[Hybrid: Indonesia, Australia, Papua New
Guinea]
Annular 134 0.952
05m17s N. America, C. America, S. America
[Annular: w US, C. America, Columbia, Brazil]
Total
139 1.057
04m28s N. America, C. America
[Total: Mexico, c US, e Canada]
Annular 144 0.933
07m25s Pacific, s S. America
[Annular: s Chile, s Argentina]
Partial 149 0.936
nw Africa, Europe, n Russia
Partial 154 0.853
s Pacific, N.Z., Antarctica
Annular 121 0.963
02m20s s Argentina & Chile, s Africa, Antarctica
[Annular: Antarctica]
Total
126 1.039
02m18s n N. America, w Africa, Europe
[Total: Arctic, Greenland, Iceland, Spain]
Annular 131 0.928
07m51s S. America, Antarctica, w & s Africa
[Annular: Chile, Argentina, Atlantic]
Total
136 1.079
06m23s Africa, Europe, Mid East, w & s Asia
[Total:Morocco, Spain, Algeria, Libya, Egypt,
Saudi Arabia, Yemen, Somalia]
Annular 141 0.921
10m27s e N. America, C. & S. America, w Europe, nw
Africa [Annular: Ecuador, Peru, Brazil,
Suriname, Spain, Portugal]
Total
146 1.056
05m10s SE Asia, E. Indies, Australia, N.Z.
[Total: Australia, N. Z.]
Partial 151 0.871
N. America, C. America
Partial 118 0.458
Arctic, Scandanavia, Alaska, n Asia, n Canada
Partial 156 0.230
s Chile, s Argentina
Partial 123 0.891
s Argentina, s Chile, Antarctica
Annular 128 0.944
05m21s Europe, n Africa, Mid East, Asia, Arctic, Alaska
[Annular: Algeria, Tunesia, Greece, Turkey,
Russia, n. China, Japan]
Total
133 1.047
03m44s s Africa, s Indian Ocean., E. Indies, Australia,
Antarctica [Total: Botswana, S. Africa, Australia]
[1] Greatest Eclipse is the time at minimum distance between the Moon's shadow axis and Earth's center.
[2] Hybrid eclipses are also known as annular/total eclipses. Such an eclipse is both total and annular
along different sections of its umbral path.
Chapter 5
Astronomy 110
Motions of the Sun and the Moon
10
60
[3] Eclipse magnitude is the fraction of the Sun's diameter obscured by the Moon. For annular eclipses, the
eclipse magnitude is less than 1; for total eclipses, greater than or equal to 1. The value listed is Moon’s
apparent diameter divided by the Sun’s.
[4] Central Duration is the duration of a total or annular eclipse at Greatest Eclipse (see 1).
[5] Geographic Region of Eclipse Visibility is the portion of Earth's surface where a partial eclipse can be
seen. The central path of a total or annular eclipse is described inside the brackets [].
This information and more can be found at http://sunearth.gsfc.nasa.gov/eclipse/eclipse.html
Lunar Eclipses
Eclipse Predictions by Fred Espenak,NASA/GSFC
Date
Type
2005 Apr 24
2005 Oct 17
2006 Mar 14
2006 Sep 07
2007 Mar 03
Penumbral
Partial
Penumbral
Partial
Total
141
146
113
118
123
-0.139
0.068
-0.055
0.189
1.238
2007 Aug 28
Total
128
1.481
2008 Feb 21
Total
133
1.111
2008 Aug 16
2009 Feb 09
2009 Jul 07
2009Aug 06
2009 Dec 31
2010 Jun 26
2010 Dec 21
Partial
Penumbral
Penumbral
Penumbral
Partial
Partial
Total
138
143
110
148
115
120
125
0.813
-0.083
-0.909
-0.661
0.082
0.542
1.262
2011 Jun 15
Total
130
1.705
2011 Dec 10
Total
135
1.110
2012 Jun 04
2012 Nov 28
2013 Apr 25
2013 May 25
2013 Oct 18
2014 Apr 15
Partial
Penumbral
Partial
Penumbral
Penumbral
Total
140
145
112
150
117
122
0.376
-0.184
0.020
-0.928
-0.266
1.296
2014 Oct 08
Total
127
1.172
2015 Apr 04
Total
132
1.006
2015 Sep 28
Total
137
1.282
2016 Mar 23
2016 Aug 18
2016nSep 16
2017 Feb 11
2017 Aug 07
2018 Jan 31
Penumbral
Penumbral
Penumbral
Penumbral
Partial
Total
142
109
147
114
119
124
-0.307
-0.992
-0.058
-0.031
0.252
1.321
2018 Jul 27
Total
129
1.614
2019 Jan 21
Total
134
1.201
Chapter 5
Saros
Astronomy 110
Fractional
coverage
Eclipse
Duration
(Totality
Duration)
Locations where visible
00h58m
01h33m
03h42m
(01h14m)
03h33m
(01h31m)
03h26m
(00h51m)
03h09m
01h02m
02h44m
03h29m
(01h13m)
03h40m
(01h41m)
03h33m
(00h52m)
02h08m
00h32m
03h35m
(01h19m)
03h20m
(01h00m)
03h30m
(00h12m)
03h21m
(01h13m)
01h57m
03h23m
(01h17m)
03h55m
(01h44m)
03h17m
(01h03m)
e Asia, Aus., Pacific, Americas
Asia, Aus., Pacific, North America
Americas, Europe, Africa, Asia
Europe, Africa, Asia, Aus.
Americas, Europe, Africa, Asia
e Asia, Aus., Pacific, Americas
c Pacific, Americas, Europe, Africa
S. America, Europe, Africa, Asia, Aus.
e Europe, Asia, Aus., Pacific, w N.A.
Aus., Pacific, Americas
Americas, Europe, Africa, w Asia
Europe, Africa, Asia, Aus.
e Asia, Aus., Pacific, w Americas
e Asia, Aus., Pacific, Americas, Europe
S.America, Europe, Africa, Asia, Aus.
Europe, e Africa, Asia, Aus., Pacific, N.A.
Asia, Aus., Pacific, Americas
Europe, e Africa, Asia, Aus., Pacific, N.A.
Europe, Africa, Asia, Aus.
Americas, Africa
Americas, Europe, Africa, Asia
Aus., Pacific, Americas
Asia, Aus., Pacific, Americas
Asia, Aus., Pacific, Americas
e Pacific, Americas, Europe, Africa, w Asia
Asia, Aus., Pacific, w Americas
Aus., Pacific, Americas
Europe, Africa, Asia, Aus., w Pacific
Americas, Europe, Africa, Asia
Europe, Africa, Asia, Aus.
Asia, Aus., Pacific, w N.America
S.America, Europe, Africa, Asia, Aus.
c Pacific, Americas, Europe, Africa
Motions of the Sun and the Moon
11
61
Date
Type
2019 Jul 16
2020 Jan 10
2020 Jun 05
2020 Jul 05
2020 Nov 30
2021 May 26
Partial
Penumbral
Penumbral
Penumbral
Penumbral
Total
139
144
111
149
116
121
Fraction
al
coverag
e
0.657
-0.111
-0.399
-0.639
-0.258
1.016
2021 Nov 19
2022 May 16
Partial
Total
126
131
0.978
1.419
2022 Nov 08
Total
136
1.364
2023 May 05
2023 Oct 28
2024 Mar 25
2024 Sep 18
2025 Mar 14
Penumbral
Partial
Penumbral
Partial
Total
141
146
113
118
123
-0.041
0.128
-0.127
0.090
1.183
2025 Sep 07
Total
128
1.367
2026 Mar 03
Total
133
1.155
2026 Aug 28
2027 Feb 20
2027 Jul 18
2027 Aug 17
2028 Jan 12
2028 Jul 06
2028 Dec 31
Partial
Penumbral
Penumbral
Penumbral
Partial
Partial
Total
138
143
110
148
115
120
125
0.935
-0.052
-1.063
-0.521
0.072
0.394
1.252
2029 Jun 26
Total
130
1.849
2029 Dec 20
Total
135
1.121
2030 Jun 15
2030 Dec 09
Partial
Penumbral
140
145
0.508
-0.159
Chapter 5
Saros
Astronomy 110
Eclipse
Duration
(Totality
Duration)
02h59m
03h08m
(00h19m)
03h29m
03h28m
(01h26m)
03h40m
(01h26m)
01h19m
01h05m
03h39m
(01h06m)
03h30m
(01h23m)
03h28m
(00h59m)
03h19m
00h59m
02h23m
03h30m
(01h12m)
03h40m
(01h43m)
03h34m
(00h55m)
02h25m
-
Locations where visible
S.America, Europe, Africa, Asia, Aus.
Europe, Africa, Asia, Aus.
Europe, Africa, Asia, Aus.
Americas, sw Europe, Africa
Asia, Aus., Pacific, Americas
e Asia, Australia, Pacific, Americas
Americas, n Europe, e Asia, Australia, Pacific
Americas, Europe, Africa
Asia, Australia, Pacific, Americas
Africa, Asia, Australia
e Americas, Europe, Africa, Asia, Australia
Americas
Americas, Europe, Africa
Pacific, Americas, w Europe, w Africa
Europe, Africa, Asia, Australia
e Asia, Australia, Pacific, Americas
e Pacific, Americas, Europe, Africa
Americas, Europe, Africa, Asia
e Africa, Asia, Australia, Pacific
Pacific, Americas
Americas, Europe, Africa
Europe, Africa, Asia, Australia
Europe, Africa, Asia, Australia, Pacific
Americas, Europe, Africa, Mid East
Americas, Europe, Africa, Asia
Europe, Africa, Asia, Australia
Americas, Europe, Africa, Asia
Motions of the Sun and the Moon
12
62
Chapter 5
Astronomy 110
Motions of the Sun and the Moon
13
63
Calendars and Time
One of the earliest and most important functions of astronomy is to provide information for a
calendar. Most civilizations want to keep track of the seasons, which depend in turn on the
declination of the Sun. But the declination of the Sun changes slowly and it is not always obvious
when the Sun gets to one or another extreme of its motion. On the other hand, changes in the
Moon’s phase are very obvious and easy to keep track of. It would be nice if these changes could both be used to keep track of things.
Alas, the moon requires 29.53… days to go through its cycle of phases, while the seasons (including accounting for precession) repeat every 365.2419…days, every tropical year. The
lunar synodic period (as the time for phases is called) will not divide into the tropical year
evenly, without a fraction of remainder. The tropical year is between 12 and 13 lunar months.
Worse yet, neither the lunar month nor the tropical year is an integer number of days. But no one
wants to start the year in the middle of the day (like 11 AM for example) and then try to keep track
of the date.
Ancient civilizations generally tried to reconcile the lunar and solar cycles.
In Egypt, it was most important to keep track of the flooding of the Nile. This occurs on a yearly
basis, due to rains flowing into the southern parts of the river. Seed had to be sowed before the
flood covered the fields, providing the only water of the year. So it was necessary to know when
the Nile would flood, well in advance of the actual event.
The Egyptians used a 365-day solar year for the civil calendar. It was constructed by using 12
months of 30 days each plus 5 extra holiday days. This preserved the idea of the 29.5-day lunar
month, but does not keep the lunar phases aligned with days of the month.
As the ~1/4 day difference between the civil and tropical year accumulated, the Egyptians
realized that they had a problem. They decided to use the heliacal rising of Sirius to trigger the
year. Heliacal rising is when the body rises just before the glare of sunlight makes it impossible to
see. The next day, the same celestial body will normally rise ~3min 56 seconds EARLIER and will
be visible during the night for a while. This method of keeping the calendar IS affected by
precession, but on a much longer time scale.
Q 1) If you used the Egyptian 365 day calendar, about how long would it take for the calendar to get 30 days out of
alignment with the Sun?
2) If you used the Egyptian 365 day calendar, about how long would it take for the calendar to get a whole year out of
alignment with the Sun?
3) What date would you estimate that Sirius rises just before the Sun these days? (Make a horizon for the Earth and move
the earth around until the dawn horizon just touches the Sun. Now estimate the date?)
4) What date would you estimate that Arcturus rises just before the Sun these days?
In 238 BCE the Egyptian calendar was reformed by including leap years, with 366 days, every
fourth year, bring the average length of the year to 365.25days.
Lunar calendars were in use in the Middle East at the same time. To keep the seasons aligned
with the lunar months, some years need to have 12 lunar months, and others need to include 13.
This is done by having another, intercalary month, every 2.8 years on the average. Calendars like
the Chinese, Vietnamese, and Jewish ceremonial calendars all work this way. Each of these
calendars has its own distinct new year time and scheme for intercalation. These calendars are
never allowed to slip far from the seasons.
The early Roman calendar also used lunar months, with additional intercalary months in the
winter. By the time of Julius Caesar, several intercalary months had been skipped and the
traditional March 25 new year had drifted far from the vernal equinox. Caesar reformed the
calendar by introducing two intercalary months for that year and by adopting the scheme of 365
Chapter 6
History –Calendars and Time
1b
days (some 30 and some 31 day months) with one leap year every 4th year. This is called the 64
Julian calendar.
The Julian calendar has an average year of 365.25 days, assuming that the leap year is properly
observed. But the tropical year, the year that stays aligned with the seasons, is only 365.2419…. days, some 0.008 days shorter. On the average the Julian calendar runs 1 full day behind the
tropical year after 1/. 008 = 125 years. After 1500 years, the Julian Calendar would predict vernal
equinox 12 days later than it actually occurred.
Perhaps no one would have cared, but the Catholic Church needed to compute when Easter
would occur. Traditionally, Easter is on the Sunday, following the Full Moon, which follows the
Vernal Equinox. This would make it 2 days after the Passover Seder (when the Last Supper
would have occurred).
It would be easy to observe the vernal equinox, then the full moon, and then have Easter
(assuming that there was a way to correct for bad weather). But people wanted to predict when
Easter should be celebrated years in advance.
Many numerical schemes were tried, and
recorded. But the discrepancy between the Julian calendar and the Jewish lunar calendar, made
it obvious that there was a problem. According to the Julian calendar, the vernal equinox got
earlier and earlier in the year.
Several attempts were made to correct the problem. People were not even certain that the
tropical year was constant. Eventually in 1582 Pope Gregory declared a solution based on the
findings of a commission he had called. In February 1582, a papal bull was sent instructing
people on how to revise the calendar. At that time, January 1 became the start of the year. The
decision was that the day following October 4, 1582 would be October 15, 1582. At that time the
current leap year scheme was adopted
Gregorian Calendar Leap Years
February 29 occurs in years
-divisible by 4 (with no remainder) EXCEPT
-century years if they are not also divisible by 400
As you may imagine, it was hard for countries to respond to a calendar change within the same
year, even if a country meant to do it. Some Catholic countries adopted the Gregorian calendar
immediately. Others adopted it later. The history timeline includes some of the dates.
Non-Catholic countries weren’t about to do what the Pope said, regardless of whether it was right or wrong. For many years different countries used different dates. So if you read European
history, the dates may be in OS, old style (Julian Calendar) or NS (new style) Gregorian dates.
Countries switched to NS one by one. Britain and the colonies changed in 1752; Russia changed
in 1917. When each area switched, the number of days skipped was altered to bring the
calendars all together with the same dates.
The Gregorian calendar isn’t perfect. It is still 26 seconds too short. But the day is getting longer as the Moon spirals away. So the discrepancy is getting smaller.
There are several calendars in use that don’t use the tropical year as a base or reference. The Islamic calendar uses 12 lunar months and never 13. So the year is complete in less than a
solar year and the holidays slip backward through all seasons. The month traditionally begins with
the actual sighting of the crescent moon as soon after new moon as is possible. To keep a
calendar that approximates this month, the 12 months have 29 and 30 days.
The Mayans kept at least three different calendars. One was a 365-day solar calendar, consisting
of 18 months with 20 days each. Another was made of 13 cycles of 20 days each for a total of
260 days. These two calendars come into alignment every 52 years, called a calendar round.
The Mayans also kept a long count consisting of a cycle of 5130 years. It is composed of shorter
20-day cycles with repeats of 20’s and 13’s.
Chapter 6
History –Calendars and Time
2b
Traditionally, classical period Mayans cosmology states that 3 of these great cycles had been 65
completed before their current cycle (which started in 3114 BCE and ends in 2012). The entire
world is supposed to end and be renewed at that time.
By this time, you may be wondering how astronomers put up with all this complexity. When we
want to find the orbit of a comet, for example, we may have data from previous years. But to
know how long ago that really was, we would need to take into account the number of February
29’s etc. that have occurred in between, whether daylight savings time was in place and how many time zones between the observation locations.
Astronomers don’t mess with this. They use a system called Julian Day. It has not months, weeks or years. It just counts days since noon on Jan 0 at Greenwich England in 4713 BCE. This day
was chosen based on the idea that it is unlikely that a historic account will be found (on Earth)
which occurs before then. Jan 1, Midnight of 2000 (at Greenwich) was 2451544.5. Within each
day, astronomers use decimals (like JD 2451544.03).
The second, based on vibrations of a Cesium atom, is the way absolute time is measured. The
Earth’s orbit and the spin are not exactly constant. The length of the nominal day was set in the 1870’s, so the reference day is not changing due to tides. Chapter 6
History –Calendars and Time
3b
66
Chapter 6 History of Astronomy-Ancient Times through Galileo
In this chapter we will be examining the way people’s concept of the Universe has evolved.
Some peoples have simply tried to predict what the sky would do and when it would do it. Others
have tried to understand the Universe by making a model and comparing what we observe with
the model’s predictions. Comparing predictions from models with observations and experimental
results is the way that science proceeds today.
There is a timeline at the back of
this chapter. It includes several
traditions of astronomy divided by
geographic location. Many of
these traditions were developed
independently. Wherever people
looked at the sky, they found a
need to explain what they saw.
Today’s concepts have evolved
from
Mesopotamia
through
Greece to Europe.
What did they see? They saw
everything that we can see today
without a telescope. This list
includes; stars and planet rising
and setting; changing points of
sunrise and sunset, phases of the
Moon, alignment of the Sun, Moon and planets compared
with the stars, comets, eclipses. We will be able to fill in the
first part of the table from what was learned in chapters 1
through 5, and the second part by the time that we finish
chapter 6. Let us follow the chronological development.
They seem to have noticed the different positions
Archeoastronomy is the study of astronomy without
written records. The date archeoastronomy ended
depends strongly on the culture involved. The Babylonians
had cuneiform writing as early as 4500 BCE, while
Hawaiians did not have writing when they were visited by
Captain Cook in 1779 CE.
Archaeoastronomers often infer astronomical significance by
finding parts of structures aligned with rising, setting, or
(more rarely) meridian passage of the Sun, moon, planets or
bright stars.
In the Great Plains (both the US and Canada), we have found ~50 structures called “Medicine
Wheels”. These are made of piles of stones laid on the ground in patterns with spokes and
circles. Typical diameters of the Medicine Wheels are ~50 feet with heights of the rock piles of
less than 2 feet. The number of spokes and circles in each varies, but alignments from one circle
to another often indicate rising and setting points of bright stars, such as Sirius and Aldebaran.
We don’t know their purpose.
Further south, native Americans living in pueblos in Arizona and New Mexico used the position of
sunset compared to distant hills to keep track of planting dates for corn. We have at least one
case where these positions were explained to an outsider. Natives of the American southwest
Chapter 6 History of Astronomy-Ancient Times through Galileo
1
67
Motion
1. Earth Spins
Observable Consequences, Remember to Identify all that Apply
2. Earth Orbits
3. Earth Precesses
4. Moon Orbits
5. Moon Spins on its
Axis
6. Planet Spins on its
Axis
7.Planet Orbits
Chapter 6 History of Astronomy-Ancient Times through Galileo
2
68
Phenomenon
Time for
Complete
Cycle
Explanation
Current Model
Explanation,
Ptolemy’s Model
1a Stars Rise and
Set
1b Sun Rises and
Sets
1c Moon Rises
and Sets
1d Planets Rise
and Set
2a Sun Moves
Along the Ecliptic
2b Sunrise and
Sunset Points
Change
2c Earth has
seasons
3a Planets have
day and night
4a Planets move
along the ecliptic
4b Planets show
retrograde motion
Some motions have a range of values, if so, say so.
Chapter 6 History of Astronomy-Ancient Times through Galileo
3
69
If the explanation won’t fit, use a separate sheet.
built many buildings with small windows aligned to specific sunrise and sunset dates, typically the
solstice and equinox. e observer.
On Fahade Butte near Chaco Canyon New Mexico, we have found two spirals carved into rock.
This is sometimes called the Sun Daggar because slabs of rock in front of the spirals cause
daggers of light to cut down through the larger spiral at noon on the summer solstice, through the
smaller spiral at noon on the equinox, and cause daggers to stay out of both spirals at winter
spiral. The edge of the slabs of rock cause the shadow of the rising moon to fall in the middle of
o
the spiral at extreme northern moonrise (Moon at +28.5 declination) and in the middle of the
o
spiral at minimum extreme northern moonrise (Moon at +18.5 declination). Fahade Butte is near
Chaco Canyon, the site of Pueblo Bonito a great Kiva with hundreds of rooms. Chaco Canyon
was a major trade and cultural center from about 1100 to 13000 CE.
Today’s Mexico, Guatemala and Belize were home to a sequence of related cultures. The Olmec,
Toltec, Mayan, and Aztec cultures seem to have evolved from one another. They built stepped
temples and ceremonial cities with similar alignments. The Mayans, in particular predicted Venus’
positions, eclipses and kept a cyclic calendar. They had writing and we are currently interpreting
their writings. Some of their writings are carved into stone, others were painted on bark paper.
Unfortunately, nearly all of the bark paper writings were burned by the settlers. Today only four
Mayan codices written on bark paper survive. They were exported to Europe and not destroyed.
Chapter 6 History of Astronomy-Ancient Times through Galileo
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70
The Dresden Codex, so named for the city where it is stored, includes tables of eclipses and of
Venus positions.
In Britain, Ireland, and Brittany (northwestern France, near the English channel), people
constructed passage graves, mounds, stone circles (made of worked stones set into the ground),
and large combined constructions like Stonehenge prior to 2000BCE. There is evidence that
these replace earlier, similar constructions, made of timbers. Statistical analyses of these
constructions show some alignments to the solstice sunrise and sunset, and possibly some to the
extreme north and south positions of the full moon rise and set. Over 1000 constructions are
known today. Stonehenge, with a diameter of nearly 100 meters is one of the more impressive,
though it has neither the largest diameter nor the largest single stone. Stonehenge was
constructed in three stages, over a period of more than 1000 years, starting around 3000BCE.
Some of its materials were brought from as far away as Wales.
The
tradition
of
astronomy leading to our
present approach began
with the Babylonians.
The
region
they
occupied is between the
Tigris and Euphrates
rivers, where Iran and
Iraq are today.
The earliest Babylonian
writing probably dates to
about 4500 BCE. The
wrote using cuneiform,
a
combination
of
phonetic and ideogram
representations
was
made of lines and
triangles impressed into
clay. The clay was dried
and
hundreds
of
thousands of examples
remain
today.
The
Babylonians
named
many
of
the
constellations of the
zodiac,
the
constellations along the
ecliptic.
They
kept
records of the motion of
the Sun and the planets
going through these
constellations
and
created formulae predicting just where planets would be. We know because tables of the
positions of Venus and Jupiter have been found, as have the formulas.
How long ago this activity started is less clear. The Babylonians kept dates in terms of number of
years into the reign of each king. The problem is that we do not yet know the entire sequence of
kings and the lengths of time that they reigned, so we don’t know the dates for sure.
Documentation of phases of the Moon and stars used to tell the time of day are found in a book
called Enum Elish, which dates to around 1600 BCE. By the 700's BCE, regular observations of
the planet's positions and of eclipses were made and recorded.
Chapter 6 History of Astronomy-Ancient Times through Galileo
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71
Babylonian astronomy stressed computing where things will appear in the sky. They used
placeholders, like our 1’s place and 10’s place. But the Babylonians used 360 divisions for a
circle and further divisions of 1/60 for each placeholder. This is where our current system of
degrees, minutes, and seconds began. This system of numbers is much easier to use for
computations than are the Greek (and Roman) number systems.
The Babylonians made careful observations and developed formulae predicting planet positions
to support their astrological practices. The astrological predictions were considered so useful, that
the observations and predictions continued even when the country was conquered.
The Babylonian view of the cosmos included a flat earth and roof like heavens called the
firmament arching above. This model doesn’t lead to mechanisms producing the observed motion
of stars or planets. It is, however, very similar to the model underlying the Bible and is similar to
some Egyptian and Greek ideas.
As
the
Babylonians
continued
their
observations, civilization grew in the Greek
mainland. The earliest indications we have of
the state of Greek astronomy are in the Iliad
and Odyssey. They include snippets of
information such as that one should plant
when the Pleiades rise at dawn. The Iliad and
Odyssey were developed over hundreds of
years, but dates for the completion of the text
is usually somewhat after 1000BCE.
Hesiod’s “Works and Days” (~ 850BCE)
includes a more formal type of star calendar called a parapegma. The parapegma associates the
days of the year to plow, plant etc. with heliacal rising (rising right before the Sun, so that the
body is just visible before daylight) of specific stars. Because of precession, the times of the year
associated with these star risings are not now exactly at the same season.
The Greeks got the idea to form theoretical models of the cosmos. Information about their
concepts has come down to us, but we have none of the Greeks original writings prior to Plato,
Around 600 BCE, a trio of Greek expatriates (folks who left Greece) lived in Miletus, a former
seaport in Asia Minor (today 8 miles inland in Turkey). They were the first to formulate theoretical
models of the cosmos.
Thales(624-547 BCE), the earliest of the Miletus astronomers, was reputed to have cornered the
market on olives. He thought that water was the most important of the four elements (earth, air,
fire, water). His model does not include any specific mechanisms to produce motions of the stars
or the Sun or Moon On the other hand there was an eclipse in 585 BCE, and Thales is said to
have predicted it and frightened Miletus' enemies in a battle.
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Anaximander's model is striking because it uses an entire sphere of stars. The star sphere
(Primum Mobile) causes the stars to rise and set while Earth stands still. He thought that the
surface of the Earth is the horizontal part of a cylinder. He modeled the stars as holes in the
Celestial Sphere, illuminated by fire surrounding the sphere. He modeled the motions of the
planets, the Sun and the moon as imagining them carried by tilted rings. His tilted rings are
similar to the observed paths of the planets, tilted compared to the celestial equator. The source
of light for the Sun, Moon, and planets was compressed air, iwithn the tilted ring. The compressed
air exits by a hole where it burst into fire, becoming visible. This model is meant to have no
beginning or end in time, but to be perfectly regular and repeatable. Perhaps this was a reaction
against the unpredictable mythological Greek gods.
Ionian School
ANAXIMANDER, MILETUS ( 611-546 aprox BCE)
*
*
CYLINDRICAL EARTH,
SUPPORTED BY AIR,
TOP MAY BE CONVEX
*
TRANSPARENT RING OF
AIR, TURNS TO FIRE AT OUTLET
WHERE SUN OR PLANET IS SEEN
LIGH
FROM
T
SUN OR
PLANE
T
*
Check
Why does Anaximander need several
yourself
Why can he use rings for the planets, Sun,
rings?
rather than entire
moon
Why are the rings tilted compared to the
spheres?
Is there any evidence of a cylindrical
sphere?
Does this model make the stars rise and
Earth?
set?
SEPARATE RING FOR
EACH CELESTIAL BODY
*
Fire surrounds the
sphere light shines through
celestial
star
as
s
Anaximenes
model, although
COSMOS HAS NO BEGINNING OR END, BUT CONTINUES INFINITELY IN TIME
CYLINDRICAL EARTH, HEIGHT = 1/3 BREADTH, PEOPLE LIVE ON TOP
SINCE EARTH IS IN THE CENTER, THERE IS NO DIRECTION TO FALL
SEPARATE CONCENTRIC SPHERES FOR SUN ( FURTHEST), STARS NEAREST
SUN, MOON, STARS ALL ILLUMINATED BY FIRE COMING THROUGH RING
SUN RING DIAMETER 27 TIMES EARTH DIAMETER SUN HOLE SAME SIZE AS
EARTH
MOON RING, DIAMETER 19 TIMES EARTH DIAMETER
later in time than Anaximander’s is simpler and predicts less.
Pythagoras (500-570 BCE) lived nearly contemporaneously. He moved to Croton (~540 BCE),
on the instep of Italy and founded a school and religion. It was a religion with secrets,
mathematical secrets. Because of the secrecy, we do not know exactly what Pythagoras
discovered and what was discovered by others later.
Pythagoras is thought to have discovered the relation between the squares of the sides of a right
2
2
2
triangle and the square of the hypotenuse (c =a +b ). He also discovered that the value of √2 is
an irrational number. That means it cannot be represented exactly by a fraction. At that time the
Greeks thought that every number could be represented exactly by the fraction. So they did not
welcome the discovery of a value which did not fit in their worldview.
The Pythagoreans thought that the planets were small bodies carried on spheres centered on the
spherical Earth. They thought that the sizes of the planets’ spheres were not arbitrary. Rather
they were determined by the relations between the notes of musical chords. If one were to listen
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(and realize that the ever-present background was the music), one would be able to hear the
“Music of the Spheres”.
At least one of their models, attributed to Philolaus, hypothesized that the Earth was not exactly
at the center of the Universe. Rather the model treats the Earth as moving around a central
spindle of fire every day. When we face the Sun, it is daytime. When we face away, it is night.
The Sun shines by reflected light from Hestia. We, Earthlings, don’t see the spindle of fire
because the counter earth, called the Anticthon, stands between Earth and the fire. The system
includes 10 bodies total, including the Sun, Moon, Earth, planets, Antichthon, and spindle of fire.
Plato (427-347 BCE) is the first of the Greeks whose writings we have today. Plato was primarily
a philosopher. He thought it was not worthwhile to make observations, because only external
features can be detected. But Plato was interested in the true nature of things, which he thought
would never be discovered in this way. On the other hand, Plato was aware of the Pythagoreans
and probably knew about Philolaus’ model.
Plato didn’t write any astronomy book. On the other hand, he described the natural world in parts
of his “Dialogues” and “Timaeus”. They
were written about 20 years apart, so it is
possible that his opinion changed
between the times of writing. Timaeus
includes a long discussion by a person
who is identified as a Pythagorean.
Whether Plato actually wrote Timaeus is
highly questionable.
Plato had the idea that the part of the
Earth known to the Greeks (the
Mediterranean) was just a small part of
the Earth and there might be other
civilizations on the Earth, of which the
Greeks were unaware. (Was he correct?)
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In Timaeus, a Pythagorean (NOT Plato) describes the physical universe as rotating around a
central “spindle of fire” which keeps it together. The planets move on concentric spheres or “lips”
or “rims” with the stars on the most distant rim. The rim where the stars are mounted moved the
opposite direction to the motions of the other bodies (Sun, Moon and planets). This is to make the
entire sky rise and set (apparent westward motion) while the planets and Sun moves eastward
against the star background. Plato seems to have known about Philolaus’ idea that the Earth
was not exactly at the center of the Universe, but rejected the idea.
Plato assigns a distance order to the planets, based on the times
they take to complete their path through the sky. He assigns two
series of numbers to their distances. 1-2-4-8 and 1-3-9-27. These
sequences do not correspond to either the actual distances or the
actual times to move along the ecliptic.
The impression of later workers is that Plato and/or Aristotle were
convinced that any valid model of the universe must have the
Earth at (near) the center (see Aristotle for why). They did not
distinguish the Sun or Moon as being very different from among the other bodies, but all the
bodies were expected to move in circles at constant speed around the Earth, which stands
still at the center. It is not clear that either Plato or Aristotle ever wrote this exactly, but later
workers tried to make models with the Earth at the center and only circular motion.
Aristotle (384-322 BCE) was Plato’s student, but unlike Plato, he did believe that science was
important and wrote many books about science. Aristotle generally believed that it was
worthwhile to observe the physical world, to find out what it would do naturally. He did not set up
controlled experiments (but that would have subjected the situation to an unnatural situation).
Aristotle had the idea that the world is made of Earth, Air, Fire, and Water. He distinguished
between areas below the Moon, where things can change and the unchanging world of the
heavens starting at the Moon and going further out. The Earth is composed of heavy things (earth
and air) which sink to their natural places as close as possible to the center of the Earth. The
heavens consist of air and fire which both float upward. He did not believe that there is any
empty space. Wherever there was no obvious material, he thought that space was filled with
ether (not the same as the anesthetic). Aristotle tried to find the nature of things. To do that, he
observed them, but did not try to do experiments or control their behavior.
Aristotle, and his predecessor Eudoxus, tried to describe all of the motions of the heavenly
bodies. Speaking generally, they and all the ancients tried explain the following motions:
a) Rising and Setting of Sun, Moon and planets
b) Sun, Moon and planets moving eastward among the stars, completing their paths
around the sky in times from 27.3 days for the Moon, to 29.42 years for Saturn
(slower than the rise and set)
c) Planets moving retrograde when opposite the Sun or when at inferior conjunction
(between Sun and Earth)
d) Sun, Moon, and planets moving eastward with varying speed at specific repeatable
parts of the sky (as measured by the position relative to the constellations of the
zodiac)
Formulating a model to predict the apparent positions of the heavenly bodies occupied
astronomers for nearly the entire next 2000 years. Aristotle thought of physical objects to make
the motions occur. He did not believe that there could be empty spaces. Other astronomers were
more satisfied with purely mathematical models to predict the positions.
Most ancient astronomers, including Aristotle, thought that the heavens were moved by a star
sphere called the Primum Mobile (meaning prime mover). The purpose of the Primum Mobile is
both to get everything moving and to cause rising and setting. Every day (23 hours 56 minutes)
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the star sphere moves WESTWARD around the stationary earth dragging all the other objects
with it. The Primum Mobile was considered so basic, that most authors do not even mention it.
Eudoxus realized that combinations of circular motion with different axes can produce retrograde
motion as seen by the Earth at the center. Eudoxus thought of a model using 27 spheres to carry
the 5 planets, the Sun, and the Moon around the Earth. Aristotle built on this model, and
expanded it to 55 spheres plus the Primum Mobile. The planets, Sun, and Moon were envisioned
as small things fixed to the spheres. Aristotle thought that spheres would spin forever, so there
would be no problem in keeping the bodies moving. Aristotle envisioned the spheres being made
of crystal (rock crystal, like quartz) so that they would be transparent.
Aristotle (384 - 322 BCE)
Primu
Mobil
m
outermost
e
,carries
bodie
all
s
*
**
*
Model of
Universe
Tilt of axes of spheres causes varying
of motion and varying directions. Can cause
rates
motio
retrograde
Cut-away of spheres for
n
visibility
Earth at center, neither rotating nor
revolving
Bod
y
Star
Satur
s
Jupite
n
Mar
r
Venu
s
Mercur
s
Su
y
Moo
n
Total
n
s
Spheres
,Eudoxus
'Mode
1
l
4
4
4
4
4
3
3
2
7
Spheres Counte
,Aristotle rrotator
's
s
Not
counted
Model
4
separately3
4
3
5
4
5
4
5
4
5
4
5
0
3
2
3
2
Tota
lAristotl
Mode
e
l
7
7
9
9
9
9
5
5
5
It may seem awkward to have everything move around the Earth, rather than assuming that the
Earth spins. Until telescopes were in use (1600’s CE), there was no reason for people to believe
that the planets were anything but little lights. So it was far easier to move them than to move the
heavy Earth. In the 200’s BCE. Aristarchus figured out the distances to the Sun and the Moon.
The combination of their distances and their appearance indicate that the Sun and Moon are
large. This may have been what led Aristarchus to believe that the Earth orbits the Sun.
Most people thought that the Earth could not be moving because
- we cannot feel it move
- we would fall off if the Earth were moving
- if the Earth moved, we would notice that we get closer to the stars on one side of
the sky for part of the year, but we don’t
- if the Earth moved, we would see parallax, but we don’t
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-Besides , the Universe is made for mankind, so why would the Earth move?
So all of these arguments combined to make most folks (including Aristotle) believe that the Earth
did not move. Why didn’t the stars look different on the different sides of the orbit? And why didn’t
they observe parallax as the Earth moves around the Sun? These effects are far smaller than
people expected and are very hard to see. It actually took until 1838 CE for anyone to see
parallax of any star. Then they picked a nearby star and lined themselves up with a chimney to
keep things straight.
The very largest parallax angle of any of the stars, is about 1/5000 degree. So it is
understandable why ancient people did not observe parallax of the stars.
Aristotle believed that the Earth is at the center of the Universe and does not move. He reasoned
that if the Earth moved, we would see parallax of the stars and the distances between the stars
would appear smaller on the side of the sky that Earth is closer to.
Aristotle and other Greeks reasoned that Earth must be spherical due to the following
observations.
First, different stars are seen at
different latitudes on the curved
earth. If the Earth were flat, the
same stars would be seen.
Second, you leave an object it
appears to disappear from the
bottom up, due to the curvature
of the Earth. On a flat Earth, things would just fade into the
mist.
During lunar eclipse, the Moon goes into the shadow of the
Moon and the curvature of the shadow can be seen.
Regardless of what part of the Earth faces the Sun and of the
declination of the Moon, the curvature of the shadow is the
same. If the Earth were any shape other shape, the shadow
would have a different curvature at least some of the time.
Aristotle wrote many of his ideas in a book called Physics. It was lost to Western Europe during
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the Dark and Middle Ages, but was retained by Islamic astronomers. When it was later translated
to Latin, it became the standard in Europe until after 1600CE. Renaissance professors were
required to teach their students how to interpret it. Aristotle’s ideas included the following.
- Heavy things fall faster than light ones
- It is necessary to keep pushing on something (on Earth) to keep it from stopping
- When you shoot an arrow, the air keeps pushing the arrow to keep it going
- When the arrow is ready to fall, it just drops vertically
- Nothing beyond the Earth’s atmosphere changes
Which of Aristotle’s ideas is correct?
Aristotle was convinced that the Earth is at the center of the Universe, unmoving. But
Aristarchus( 310-230 BCE) believed that the Earth orbits the Sun. We do not have the book, or
books which explain why Aristarchus thought the Earth moves. The idea was not accepted by
other astronomers at the time.
We do have a book of Aristarchus’ called “On the Distances to the Sun and Moon”. In it he finds
the sizes of and distances to both bodies using the methods below.
How did Aristarchus measure the distance to the Moon and its size?
o
When we look at the Moon (or the Sun) in the sky, we see that each of them is about 1/2 in
diameter.
Aristarchus measured the time it takes the moon to move through the Earth’s shadow during a
lunar eclipse and compared that time to the time for the Moon to complete an orbit.. He formed
the ratio
.
o
Aristarchus knew the times for orbit and eclipse and he knew the 360 , so he solved for the size
o
of the Earth’s shadow. He found that it takes up about 2 along the Moon’s orbit.. Since the Moon
o
takes about 1/2 , the Moon is about 1/4 as large as the Earth. Not a small thing at all.
o
Using the fact that the circumference of a circle is 2πR and the moon diameter (the 1/2 ) takes
about 1/720 of this distance, we can find that the Earth diameter is about 4/ 720 or 1/ 120 of the
distance to the Moon. We could say the Moon’s distance is about 60 times the Earth’s radius.
Aristarchus also measured the distance to the Sun In terms of the distance to the Moon. He
the idea that if he measured the angle between the Sun and Moon at the very moment when
Moon was either first or third quarter, he knew that the triangle with the Sun, the Moon and
o
Earth at each vertex would have a right angle (90 ) at the center of the Moon. He measured
got
the
the
the
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angle between the Sun and Moon as seen from the Earth.
Aristarchus’ measurement, that the Sun is 1200 Earth Radii away, is impressive, but wrong.
Interestingly, it was not challenged for at least 1800 years. The measurement was wrong
o
o
because the angle at the Earth should not be 87 (leaving 3 for the angle at the Sun). The angle
5
o
1
o
at the Earth should have been 89 /6 leaving /6 for the angle at the Sun. The corrected
measurement puts the sun 400 times as far as the Moon or 400x60=24,000 times the Earth
o
radius. Since the Sun appears to be 1/2 across, the great distance means that the Sun is far
larger than the Earth or Moon. So from Aristarchus’ point of view, it would have made sense to
move the Earth rather than move the Sun and Moon.
Aristarchus did not know the size of the Earth. It took Eratosthenes to find it.
Eratosthenes had heard that at Syene, upriver on the Nile, the Sun is at the zenith at noon one
day of the year. Eratosthenes lived at Alexandria, on the Mediterranean Sea, where he knew that
the Sun never reaches the zenith. Eratosthenes believed in the spherical Earth, and he assumed
that the sunlight comes in parallel rays. So he expected that the difference in the direction of the
sunlight was due to the curve of the Earth.
He got the idea to measure the angle between the surface of the Earth at Alexandria and at
Syene. Eratosthenes stuck a stick, called a gnomon, into the ground at Alexandria. Sunlight
came in at an angle to the stick, causing a shadow. He
measured the length of the stick and the length of the shadow.
sunlight
o
There was a 90 angle between the stick and the shadow. So
makes the
o
he could complete the triangle and measure the angle at the
hypotenuse 90 gnomon
o
top. He got an angle of 7.1 .
shadow
The angle between the stick and the sunlight is the same as the angle at the center of Earth with
one end at Alexandria and the other at Syene. Eratosthenes knew that the ratio of the distance
between Alexandria and Syene (the 5000 stades) to the Earth’s circumference is the same as the
o
ratio of the angle at the center of Earth to 360 .
We do not know the exact location of the gnomon at Alexandria. Neither do we know the exact
size of the stade. So we do not know exactly how accurate Eratosthenes measurement was.
Estimates are that it is accurate to within ~10%.
So by the 200’s BCE, the Greeks had a good idea of the size of the Earth and the Moon. They
know that the Earth was not nearly the largest part of the Universe.
Aristotle’s model for planetary motions did not survive to modern times. The tilted, counter
rotating spheres were replaced by a method to produce retrograde motion using epicycles, that
is, circular motions on top of other circular motions. Hipparchus (~150BCE) developed this
method, first discovered by Apollonius (~225 BCE) to model the Universe. Hipparchus also made
the first star catalog to use the magnitude scale of star brightness and he realized that the
position of the Sun at the Equinox was changing. This led Hipparchus to the discovery of
precession.
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Hipparchus’ and Ptolemy’s Models
Both Hipparchus and Ptolemy used four separate features to explain the motions of the planets
(and Sun and Moon) that they had observed. The model is explained, feature by feature below.
Hipparchus and Ptolemy (and Aristotle and earlier astronomers) used the Primum Mobile to
cause all bodies to rise and set daily. All the celestial bodies were carried by the Primum Mobile.
The separate motions of the planets, Sun and Moon were imposed on top of the motion of the
Primum Mobile.
To envision the way that the Primum Mobile works, imagine a merry-go-round. In Hipparchus’
and Ptolemy’s view the Earth is in the middle not moving. This is like the merry-go-round operator
standing in the middle on the ground, unmoving. The floor of the merry-go-round moves quite fast
carrying everything on the ride past the operaor. The floor is like the Primum Mobile. As it goes
by, the horses and kids pass in and out of view, like rising and setting.
To model the motion of each body near the ecliptic, each body was given a separate path around
the Earth, RELATIVE to the Primum Mobile. This path, called the deferent, carries the bodies
eastward through the sky, near the ecliptic.
Continuing to compare the model to a merry-go-round, you are still the operator. Motion of the
planets on the deferent is like the motion of people walking on the merry-go-round floor in the
direction opposite to the spinning. The people go slowly compared to the floor. Each time the floor
passes you (rising and setting), the people are at a little different position compared to the fixed
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horses and poles. Eventually the people go past every one of the horses and return to the same
position. This is like each of the planets (or the Sun or Moon) completing its path along the
ecliptic.
To make the body move retrograde, each body was modeled moving on an epicycle, on top of
the deferent. So for Each body, Hipparchus defined the relative size and timing of the Primum
Mobile, a deferent, and an epicycle.
Returning to the merry-go-round model, the epicycle is what would happen if the people walked in
little circles as they walked along. Some of the time the person is moving backward part of the
time, when compared to the horses etc (all the time the floor is causing the person rise and set).
The epicycle model, with
the Primum Mobile, an
epicycle, and a deferent
for each body produces
rising and setting, motion
of the planet eastward
through the stars, and in
regular retrograde loops.
But each planet does not
have the exactly the same
retrograde motion every
time. Hipparchus knew
this and modeled the
irregular speed and loop
size by moving the
deferents so the Earth
was off-center (called
eccentrics).
Hipparchus’ writings have
not survived. We know
about his work from the
work
of
other
astronomers, especially from the work of Ptolemy (100-170 CE). Ptolemy’s work has survived.
Ptolemy’s most famous work is the Almagest, a compendium of models using epicycles, a
revised star catalog, revised estimates of the rate of precession, and information on how to use
the computations for astrological purposes.
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Ptolemy used the same kind of model as did Hipparchus for the Primum Mobile, the deferent, and
the epicycle. He used equants to cause both the speed of motion through the stars and the size
of the retrograde loops to vary. The Earth is to one side of the center and an imaginary point
called the equant is at an equal distance on the other side.
The motion of the center of the epicycle on the deferent has an angular speed which appears to
be constant from the equant. (The actual speed in space would not be constant.) Since the Earth
is not at the equant, the speed of the center of the epicycle appears to change, going more slowly
when the planet is further from the Earth and more rapidly when the planet is nearer the Earth.
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Ptolemy understood that Mercury and Venus never appear at midnight. Instead they are roughly
o
o
in the same direction as the Sun (to within about 27 for Mercury and to within 46 for Venus. To
ensure this alignment, Ptolemy introduced a linkage between the Sun and each of these inner
planets to ensure that they would stay in the same part of the sky. It is not clear whether he
believed the linkage to be a physical object, or just a mathematical concept. Ptolemy figured out
the sizes, start times, and the speeds for the Primum Mobile, and the deferents, epicycles and
equants for each of the planets and the Sun and Moon. He did not have any observational reason
to decide the overall size of the orbits, so he made the orbits just large enough that the planets on
their epicycles did not hit one another. He used Aristarchus' estimate for the Sun's distance. The
relative size of the epicycle compared to the deferent is determined by the apparent size (the
angle) of the retrograde motion in the sky.
To use Ptolemy's model one has the start time etc for each body, and can figure out the position
for any time in the future by adding up the motion of the Primum Mobile, the deferent and the
epicycle. The equant is used to find the position of the center of the epicycle. Ptolemy wrote out
tables in his books to help astronomers use the model to predict positions with less work. Some
of these tables are included in the Almagest and in a book called “Handy Tables”.
After Ptolemy died, Western Europe did not produce much innovation in astronomy. The Romans
did not promote new science; in fact, the closest to a scientist we know of are compilers of
scientific knowledge. The last Roman emperor was deposed in 476CE and the museum and
library at Alexandria were lost its last member near 400CE, leaving the west detached from many
o f the writings
and works of the Greeks, including Ptolemy, Aristotle and Plato.
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Astronomy was useful for finding the correct direction to Mecca (for prayer), for computing when
the waxing crescent moon should first be visible to start the month, and for computing the time in
the patient’s horoscope to perform medical procedures. Ptolemy’s models were used to make the
predictions. In fact most of the star names we use today are Arabic names given by the Islamic
astronomers. The Islamic astronomers observed the stars and planets and compared their
positions with the predictions. As the observed positions came to differ from the predictions in the
Almagest, they made revised tables called zij’s. The principals of prediction, the Primum Mobile,
deferent, epicycle and equant were the same; the number values were different.
As Europe awoke from the Dark Ages, works of the Greeks were translated from Arabic into the
Latin of the educated classes. Plato, Aristotle, and Ptolemy were taken as great authorities.
Ptolemy’s works were studied (and simplified to enhance understanding) and the tables were
revised repeatedly.
Nicolas Copernicus (1473-1543) was born in Torun, Poland. He was educated at universities in
Cracow, Bologna (canon law and astronomy), Padua (medicine), and got a degree in canon laws
from the University at Ferrara. His uncle was Bishop of Ermeland. Copernicus was employed as
secretary and physician to his uncle while the bishop was alive. He held the post of canon of
Frauenberg cathedral for his entire life. After his uncle’s death he continued at Frauenberg, acted
as a consulting physician, studied astronomy, served in reforming the currency and negotiating in
the wars between Poland and Prussia.
It is not certain when Copernicus got the idea of letting the stars stand still, and letting the Earth
rotate (giving the impression of rising and setting) and having all the planets orbit the Sun. He
was aware of Aristarchus’ beliefs, but did not have Aristarchus’ writings concerning the motion of
the Earth. Copernicus was particularly disenchanted with the equant.
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Copernicus wrote a brief summary of his theory, the Commentolarius (1510-1514?) and
corresponded with other academics discussing his theory. During Copernicus’ life even the Pope
knew about the theory (1536). Copernicus was concerned because his theory conflicts with the
Bible. His colleagues in the Church encouraged him to document his theories and predictions.
Their approach was that if the theory was correct, it would be reconciled with the Bible properly
interpreted. Meanwhile it would be worthwhile to explore the theory and examine its correctness.
Copernicus delayed publishing his work. He was visited by Rheticus, a German mathematician,
Rheticus. Rheticus was impressed by the theory, and with Copernicus’ permission, wrote a brief
summary of Copernicus’ work. It was published and went into two printings. There were no
negative repercussions. Copernicus was getting old, and he wrote up his life’s work in a book
called “de Revolutionibus Orbium Coelestum (About the Revolutions of the Celestial
Spheres)". Copernicus completed the manuscript and sent it to Rheticus to prepare it for printing.
Rheticus handed the work to Osiander, a Lutheran theologian.
Osiander (and Martin Luther) did not think that the world needed a theory of the universe
separate from the information in Genesis. Osiander encouraged Copernicus to portray his model
as just another way to compute the positions of the heavenly bodies, not an approach to finding
the “truth” of the construction of the Universe. Copernicus did not take this advice, but Osiander
wrote, and included, an unsigned preface to de Revolutionibus, expressing this very sentiment..
De Revolutionibus was published in the spring of 1543. Copernicus suffered a stroke in
December of 1542, so he probably did not know of the preface. After Copernicus’ death, his
friends realized what had happened, but still the preface was not changed.
Copernicus’ model of the Universe puts the center of the Earth’s orbit at the center of the
Universe. The Sun is near that point. The Earth spins on its axis and all the planets orbit the
center of the Earth's orbit.. The orbits were circular with basically constant rate motion.
Retrograde motion occurs as a natural consequence of the fact that the planets complete their
orbits in differing lengths of time. As one planet passes another, observers both the inner and the
outer planet see retrograde motion.
Chapter 6 History of Astronomy-Ancient Times through Galileo
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Copernicus
knew,
however, that the planets appear to change speed even when not in retrograde motion. Uniform
speed motion on circular orbit will not make this happen. To model the changing speed,
Copernicus introduced many small epicycles.
In Copernicus’ model, the stars are assumed to be fixed on a
sphere. Precession and changes in the amount of the tilt of
the Earth are caused by changes in the direction of the
Earth’s axis.
Copernicus’ model made it possible to determine the sizes of
the planets’ orbits in terms of the size of the Earth’s orbit.
Copernicus included sizes of the orbits in de Revolutionibus.
Copernicus made some observations to support his models
and developed new computational devices to predict the
positions of the planets. After Copernicus’ death, these
computations were used even by those who did not believe
that his models were correct. At that time (and before) the
astronomer’s job was thought to be predicting the positions of
celestial bodies. Explaining what lay behind the position
computations was thought to be the realm of physics or
philosophy.
Generally Copernicus’ models were about as accurate as the
Ptolemaic models, assuming that the Ptolemaic models were
updated with new data. So most people did not believe that
Copernicus was right. They were not anxious to demote the
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Earth from the center of the Universe to being just one among lots of planets. There was still the
problem of conflict with the Bible. There was no good explanation of why parallax was not seen
(Copernicus just said that the stars were too distant for parallax to be seen.). So few people
accepted Copernicus model.
Tycho Brahe (1546-1601) was among the astronomers who did not accept Copernicus’ model.
He tried to measure parallax for stars, but could not find any. So he would not accept that the
Earth moves.
On the other hand, Brahe did not accept Aristotle's contention that the heavens from the moon on
out are unchanging. He found that comets could not be in the atmosphere (as Aristotle had said)
because he could not measure any parallax. Since comets come and go, move among the stars
etc. the heavens cannot be unchanging. Tycho observed a supernova in Cassiopeia, a star that
brightened and faded. Both these phenomena change, but are not within the Earth's
atmosphere.
Tycho Brahe was born a Dane. He observed the planetary positions at an early age and realized
that the planets were not at the places predicted at the time predicted. So he thought he could
make better predictions using his own model. His model has the Sun and the Moon orbit the
Earth. The other planets orbit the Sun and are carried with the Sun as it moves around the Earth.
The stars are on a sphere centered on the Earth.
Because he was Danish, and well known as a scientist, the Prince of Denmark lent him the island
Hven in 1576. This island is near the coast of Sweden (and now is part of Sweden). The
Chapter 6 History of Astronomy-Ancient Times through Galileo
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agreement was for Tycho to collect rent from the farmers on Hven to support himself, to carry on
astronomical research (for the glory of Denmark) and to maintain the lighthouse.
Tycho Brahe moved to Hven and set up the first professional observatory in Europe. He built two
separate buildings, Uraniborg and Sterneborg to house his instruments and records He built very
large instruments allowing very accurate observations. Tycho was able to get observations
precise to 1 minute of arc, that is 1/60 of a degree. Tycho hired helpers and they made
observations for about 20 years. During that time the Prince of Denmark died and was succeeded
by his son. The son was less interested in astronomy and less fond of Tycho Brahe. The farmers
were annoyed with the high rents and Tycho is reputed to have taken poor care of the lighthouse.
In 1597 Tycho Brahe was forced to leave Hven. He settled briefly at Hamburg, then moved on.
Tycho found a new post as the Imperial Mathematician to Prince Rudolph of Prague (1599), so
there he went. He brought many of the instruments for measuring the positions of the stars, since
they were portable. (Obviously he didn’t bring the buildings, and unfortunately they burned down
shortly after Tycho left.)
Tycho made no more observations once he reached Prague. He tried to use the ones he had to
develop tables to predict planet positions using his model. He hired helpers to make the tables. In
1600, he hired Johannes Kepler and set him to work on the planet Mars.
Johannes Kepler (1571-1630) was a German Lutheran. He originally wanted to be a clergyman,
but was trained in mathematics and astronomy. One of the themes of his life was to find the
meaning and structure in the universe. He obtained a job teaching, but his lectures were not
attended.
Kepler noticed that that if the sizes of the planets’ orbits in de Revolutionibus are represented by
spheres, then the spheres could be fitted between the five known and possible three dimensional
perfect solids. This is similar to two-dimensional inscribed and circumscribed polygons.
The perfect solids have all of their faces the same and each edge of each face is the same.
These solids had been known since the Greeks.
The perfect solids have all of their faces the same and each edge of each face is the same.
These solids had been known since the Greeks. They consist of the tetrahedron (4 triangular
faces), the cube (six square faces), the octahedron (8 equilateral triangles), the icosahedron
(twelve pentagons), and the dodecahedron (20 equilateral triangles) There are only five such
perfect solids in Euclidean geometry, and Kepler knew it.
Kepler reasoned that if the sizes of the
planets’ orbits in de Revolutionibus are
represented by spheres, then spheres of
the sizes of the orbits for all six planets
(Mercury, Venus, Earth, Mars, Jupiter, and
Saturn) would fit with the perfect solids
between them as spacers. Kepler thought
that he had found the divine plan for the
Universe; just 6 planets with spacing
determined by the five (and only five)
perfect solids.
Kepler published his theory in a book called
Mysterium Cosmographicum (1597). He
wasn’t 100% happy with the values of the
orbital sizes in de Revolutionibus. So
Kepler sent a copy of Mysterium
Cosmographicum to the man who had the
Chapter 6 History of Astronomy-Ancient Times through Galileo
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world’s best observations, Tycho Brahe. Kepler hoped that these observations would allow him to
prove that the sizes of the planets’ orbits fit with the perfect solids between them as spacers.
Fortunately Tycho Brahe, the man with the best observations, was looking for help. He hired
Kepler to work on his observations expecting Kepler to prove Brahe’s own model.
Kepler and Tycho Brahe did not get along. Brahe did not immediately give Kepler all of the
observations he needed. Kepler got so frustrated that he went back to Germany once. In 1601
Tycho Brahe died and Kepler got possession of the observations. Kepler was given Brahe’s job
as Imperial Mathematician, but at a much lower salary than Brahe got.
Kepler knew how accurate Brahe’s observations were, so he could not simply assume that they
were in error. He was forced to abandon the idea of circular motion, or motion carried on spheres
and to adopt his three laws.
Ellipses are described by a formula involving the squares of the coordinates. You may have seen
it in the form
, where a is the semimajor axis and b is the semiminor axis. Ellipses
have two axes of symmetry. That means they can be folded along either the major or the minor
axis and the sides will match (the fact that it would not matter if -x were substituted for x, or if -y
were substituted for y, shows this symmetry). The shape of an ellipse is rounded everywhere;
there are no straight parts and no points. The foci (the plural of focus) are on the major axis and
at positions that depend on the shape of the ellipse.
The semimajor axis tells the overall size of an ellipse. In fact the semimajor axis is the average
distance of one body from the other. It is like the radius of a circle.
Chapter 6 History of Astronomy-Ancient Times through Galileo
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Ellipses come in a variety of shapes, ranging from a circle to a very elongated shape nearer a
cigar. The eccentricity tells how close to a circle it is, the larger the eccentricity, the more
elongated the ellipse.) The orbits of the planets are very nearly circles. In fact, if it were not for the
fact that the Sun is not at the center, it would be very hard to tell these ellipses from circles by just
looking at the shapes.
Kepler did not really know why these laws were correct. The laws do, however give substantially
more accurate prediction than did Copernicus’ model. Today we know that these laws describe
the motion of one body around another (laws 1 and 2) under the influence of gravity. The third law
is appropriate for the motion of several small bodies around one more massive one, also under
the influence of gravity. These laws could be derived from Newton’s work.
Kepler was not persecuted for these laws, even though they do not have the Earth at the center.
Probably this was because few people read or understood his work.
Kepler tried to explain why the planets orbit the Sun. The only force known at the time that acts
without touching the other body was magnetic force (like when the refrigerator magnet tries to
reach the refrigerator door before touching it). So Kepler tried to use magnetic attraction between
the Sun and the planets to cause them to move in orbits.
Kepler used the models to develop tables, called the Rudolphine Tables, in honor of his (and
Brahe’s) patron Prince Rudolph of Prague. He went on to develop a new type of telescope
(different from Galileo’s), He learned that stars appear above further above the horizon than
predicted, since their light is bent by Earth’s atmosphere. And he computed many horoscopes.
He still tried to find the overall plan of the Universe, later using musical harmonies rather than
perfect solids.
Galileo Galilei (1564-1642) was a contemporary of Kepler’s (they did not meet, but they did
correspond). Galileo was a northern Italian, born to a musical family. Galileo had one brother and
three sisters. His father sent him to university to become a physician so that he would earn
money and be able to pay the sisters’ dowries. The need to pay doweries may be what lead
Galileo to put himself forward and seek favor at times when others would have been modest.
Galileo quickly decided that mathematics and astronomy were much more interesting than
medicine and declined to become a physician. So he switched from the university at Pisa and
went to Florence to study mathematics.
Galileo obtained a job teaching at Pisa after he finished university. Later he moved to Padua, the
leading university of the day. He was supposed to teach Aristotle’s physics and Ptolemy’s models
Chapter 6 History of Astronomy-Ancient Times through Galileo
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of the cosmos. Those were the accepted theories. Galileo performed experiments, however,
including measuring the time for various bodies to fall. He found that the time to fall did not
depend on the mass of the body (but feathers and leaves still fall slowly. Why?). This lead Galileo
to conflicts with the scientific establishment.
Galileo discovered that a pendulum takes the same length of time to swing, regardless of how
high it swings. You have probably experienced this when pushing someone in a swing. You push
at the same time interval, regardless of how high they go. The time for the pendulum to swing
depends only on the length of the string and the gravity of the Earth. Using this principal, Galileo
devised an apparatus to time a patient’s pulse.
Galileo spent many years studying the motion of falling bodies with their variable speed. Galileo
slowed down the fall, to make it easier to measure, by rolling bodies down slopes. He found that
bodies could roll to the same height they had come from. This is known as Galileo’s law of inertia.
He tried to describe the variation of speed that falling bodies undergo.
Galileo believed that Copernicus was correct and that the Earth moves. His reasoning was based
on his personal theory of tides. Galileo thought that tides were caused by water sloshing around
as it “turns the corner” from going the same direction due to both the Earth spinning and the Earth
orbiting to the part of the Earth where it is moving opposite the direction that the Earth is orbiting.
This model is NOT correct, but it motivated Galileo.
Galileo heard that in Holland, two lenses had been used together and with the result that the
image was much magnified. He was living at Venice at the time, where there was (and is) a
tradition of glass making. Galileo had many lenses made, and hit upon a telescope made of a
weak objective lens and stronger, diverging, eyepiece lens. Galileo’s telescope magnified more
than had the work others had made (over the years Galileo made other, better telescopes).
Galileo immediately made a telescope and gave it to the City of Venice. This allowed them to see
whether grain boats or enemy ships were approaching on the Adriatic Sea. This was very
advantageous for the city. Knowledge of enemy ships allowed them to raise a chain across the
entrance to the Venice lagoon. This would break up the hull of the enemy ship. The City offered
Galileo a job for life (which he took, but later got a more lucrative position at Florence).
Galileo built several telescopes. They might go for $20 from Toys R Us today. They magnified
about 20 times and had diameters about 1.5 inches.
Galileo turned his telescope to the heavens and quickly found that
- The Moon has mountains and craters, unlike the perfection predicted by Aristotle
- The Milky Way is made of lots of stars that had never before been seen
- Jupiter is accompanied by four moons. So NOT every body in the Universe circles
the Earth (and which one has more moons?)
These discoveries were deeply disturbing to people. They differed from the status quo, and they
seem to take the Earth from its most central place, by the existence of Jupiter’s moons.
Galileo published his discoveries in Italian in a small pamphlet called “Sidereal Messenger” or
“Starry Messenger” in 1610. This was rather like publishing scientific data in a supermarket
tabloid rather than in a learned journal. Anyone could read it, and anyone could understand what
Galileo had to say. He drew pictures of the positions of Jupiter’s moons and of shadows cast by
lunar craters to explain how he interpreted what had been seen.
In 1610-11 Galileo continued his observations. He found
- Saturn has three parts. Galileo never knew what they were
- The planet Venus has phases as predicted by Copernicus’ model.
- The Sun has spots which come and go over days to weeks. The Sun rotates about
once per 25 days at the equator. It is far from perfect and unchanging.
Galileo published these results in another book in Italian, Letters on Sunspots, in 1613
Chapter 6 History of Astronomy-Ancient Times through Galileo
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In 1611 Galileo took his telescope on a trip to show others what he had seen. He went to Rome,
stopping to see astronomers on the way. Some people were convinced that Galileo was correct,
others were unable to see through the telescope very well, others refused to even look. One
astronomer, Clavius, suggested that the craters on the Moon were not the real surface. The real
surface was a smooth crystal with the craters below.
Galileo was convinced of the correctness of Copernicus’ model, but his observations show little
direct evidence and no unequivocal proof. He did try to address the issue of discrepancies
between the Copernican model and the Bible. He published a letter (1615) called “Letter to a
Duchess” designed for the Duchess Christina who had asked one of Galileo’s friends about the
Copernican Theory. This letter suggests “The Bible tells us how to go to heaven, not how heaven
goes.” What did he mean by this?
Galileo went on to write that the Bible doesn’t even mention all the planets. He thought that if
there is an apparent disagreement between the Bible and an observation in the physical world, it
must be because we do not understand what the Bible is saying. Do you think he was a religious
person or not? How do you think that others took this?
Eventually the Church decided to do something. It was not clear whether the Ptolemaic or the
Copernican theory was true, although many people in the Church were expecting that the
Copernican theory would eventually be proved true. However there was still the issue of resolving
the theory with the Bible and there still was no firm proof. In March 1616, a general proclamation
was made saying that no one (that is no one Catholic who cared what the Church did) should
teach the Copernican theory as the truth. It should only be taught as one among competing
mathematical theories. If the evidence ever accumulated to the point that the Copernican theory
was proven, then the interpretation of the Bible could be dealt with in the Church.
At this time, 1616, De Revolutionibus was banned. It was reissued in a “corrected” version with
words inserted softening the assertions that the model with the Sun at the center was “true”. A
corrected version was published in 1620. The original was banned until 1835.
In February Galileo went to Rome and had a conversation with Cardinal Bellarmine. The Cardinal
and Galileo knew one from another before Bellarmine was Cardinal. Galileo was asked whether
he believed the Copernican theory. Galileo denied that he believed it. At this time, they may have
discussed a special edict telling Galileo to refrain from discussing the Copernican theory at all.
Galileo went home with a letter signed by Bellarmine refuting the idea that Galileo had been
personally forbidden to examine the Copernican theory, but detailing the interaction.
Galileo went on with his work; Bellarmine and the Pope died. Pope Urban VIII ascended. He had
discussed the Copernican theory with Galileo years before and had held the opinion that the
Copernican might be correct. So Galileo thought that the climate might have changed.
Galileo put together his work on the “new”, non-Aristotelian physics and the Copernican model in
a book called “Dialog on Two Chief World Systems”. The book is written as a series of four days
of questions and answers. There are three characters, Sagredo, the moderator, Salviati, the
supporter of the Copernican theory, and Simplicio, a supporter of Aristotle and Ptolemy. All of
these names are names of friends of Galileo who were dead at the time the book was written.
Galileo tried to get the book approved, by giving the sensor pages as they were written. The
sensor decided that the book was too complex and the review should await the complete book.
When the book was complete, Galileo was in Florence and got permission for the censor in
Florence to do the review. The book was approved, and given the stamp of approval, the
Imprimatur.
Chapter 6 History of Astronomy-Ancient Times through Galileo
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When
“Dialog on Two Chief World Systems” was published in 1632 and copies reached the
Pope at Rome, the __ hit the fan. We don’t exactly know why, but Pope Urban VIII was angry. He
may have thought that the character Simplicio was a play on the Pope’s name, he may have
thought that Galileo had been told not to discuss the Copernican theory at all. We do know that
Galileo was summoned to Rome to be tried by the Inquisition. Galileo delayed as much as he
could and got to Rome in 1633. The Inquisition tried to recall all the copies of the book, but they
had already been sold.
Unlike American courts, where the accused must be told the charge, the Inquisition would ask the
accused what they thought the crime was. Galileo didn’t know. The Inquisition brought out a
document forbidding Galileo personally to discuss the Copernican theory at all. This was
supposedly conveyed during Galileo’s meeting with Cardinal Bellarmine in 1616. Such a
document would normally be signed by the two parties and two witnesses who would be priests.
The witnesses whose names were on this document were servants. Galileo brought out the letter
from Cardinal Bellarmine describing the meeting, and NOT showing that Galileo had been given
the edict.
The Inquisition was in a tough place. It would look really bad for them to say that they were wrong
to accuse Galileo and the Pope wanted something done.
On the other hand, Galileo was in a tough place. He didn’t want to be tortured, and he really didn’t
want to be burned at the stake. So he recanted, he swore formally that he did not believe that the
Earth moves. He was allowed to go home to his estate Arcetri (near Florence) where he was put
under house arrest for the rest of his life. His guards tried to prevent Galileo from communicating
with other scientists. Galileo continues his research into the motion of bodies. He died in
December 1642. Galileo’s books on astronomy were on the prohibited list until 1835.
In 1979 the Church convened a group which, in 1992, concluded that it had been wrong to
condemn Galileo.
Questions and Problems
1) If the Earth were flat, what would it look like as you sail away from a tree? Would it disappear
from the top down?
2) How can we tell whether an alignment is a solar alignment or a lunar alignment?
3) Redraw the picture of solar motion, like the one at the beginning of the chapter, so that it
represents the motion of the Sun as seen from Australia.
4) How did Aristotle’s model explain the Moon rising and setting?
o
5) If Eratosthenes had measured that the angle between the Sun and the gnomon was 10 rather
o
than about 7 , what would have happened to his value for the size of the
Earth.
A nswers 1) No, it should just get smaller and smaller. It might get lost in the mist before it gets
o
too small to see. 2) The moon can go to declinations about 5 further north or further south of
o
where the Sun ever rises or sets. This 5 of declination turns into 5o azimuth at the equator and
more at every other latitude 3) Leave the background, earth, sky, NSEW points all the same. The
rise and set points of the Sun could be the same, but tilt the paths toward the north.
The June 21 path should go low and in the north, the Dec 21 path should go high 4) Primum
o
Mobile carries the Moon (and everything else) in its basic daily pattern 5) Put the 10 back into
o
the ratio where 7 had been before. The distance will come out at 180,000 stades.
Chapter 6 History of Astronomy-Ancient Times through Galileo
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93
Date
Europe/Egypt/ Modern World
6000
BCE
5000
4000
3500
3000
2500
2000
Megalithic Tombs Britain and Brittany
Start date for Julian Day count Jan 1, 4713 BCE
Earliest Egyptian date found, 4241 BCE
Newgrange, Ireland Burial mound built,
Winter Solstice Sunrise alignment
Stone Circles in Britain and Brittany
Stonehenge I Started ~2700BCE, ---Stone Circles in
Britain and Brittany ----Egyptian Dynastic History,
Hieroglyphic writing
Star heliacal rising records started, calendar started
Pyramids
Three calendars, lunar phase, 365 day, and Sothis,
based on Sirius heliacal rising (Earth’s sidereal period)
36 week year, corresponding to 36 star groups
Stonehenge III complete BCE~1900 (trilithons)
Trojan War (Troy destroyed 1184 BCE)
800
Homer, Iliad, Odyssey (some date at 1000-1100 BCE)
Hesiod, Works and Days
(incl star rising and activity associations)
700
600
Babylonians adopt 7 day week
Ionian School, Thales(624-527 BCE) Earth a disk
Anaximander (611-546 BCE) Earth a cylinder
Anaximenes (585-526 BCE) Earth a disk with mountains
around it
Pythagoras (500-580 BCE), Pythagorean school ( music
of the spheres, irrational numbers) spherical earth,
crystal spheres for motion of planets, Antichton
500
China
Winter Solstice in
Aries, start Akkadian
Calendar?
1500
1000
Middle East/India
Americas
Current (not first)
Mayan great cycle
starts 3114
Earliest writing,
Mesopotamia
Empire of Hammurabi1792-1750? BCE
Venus records kept
China 2137 BCE
Hi & Ho reputedly
executed for failing
to predict eclipse
Indian lunar tables kept Chinese eclipse
records, 1400 BCE
1100 BCE Indian Solar
Tables
Earliest known Meso
American Temples
961 BCE Indian
Planetary Motion
Tables
Babylonian Day and
Night divided into 12
parts each, AND 24
equal time divisions
made.
Chapter 6 History of Astronomy - History Overview
1A
94
Date
Europe/Egypt/ Modern World
Middle East/India
China
400
Pythagorean Brotherhood 540-400
Pythagoras (c 580 -c500BCE) - spherical Earth, in center
of universe. Explained Moon phases by reflection of
sunlight. Planets move on crystal spheres.
Also Pythagorean Theorem ( sides of a right triangle),
irrational numbers (ones which cannot be represented by
fraction or decimal)
Parmenides (504-450 BCE) Theorized about spherical
Earth with zones (tropics, arctic etc. ) modeled universe
with concentric spheres
432 BCE Meton, metonic cycle discovered
(19 years=235 lunar synodic months to within 1.5 hrs)
Philolaus (~300-400 BCE) Antichton- anti earth which
prevents fire from burning us. Universe centered on
central fire.
Babylonia - Venus and
Jupiter prediction
tables
China -Star Catalog
constructed
300
Americas
Plato (427-327BCE)Thought the concept, not the
observations are important. Proposed that universal
motions are combinations of circular, constant rate
motions. Motions of bodies around central spindle. Moon
shines by reflected sunlight.
Aristotle (384-322BCE) argues spherical earth at center,
Used 56 Rotating spheres and counter rotating spheres
to make up motion. Spherical Earth explained. Divided
world into sub-lunar region where change occurs, and
super-lunar regions whereuniform circular motion repeats
forever.
Aristarchus 310-230 BCE Found Distances to Sun and
Moon, and relative Sizes of Sun, Moon, Earth
Distance to Moon, Thought Earth moves around Sun
200
Eratosthenes ( b ~273 BCE d~ 195 BCE) measured
circumference of Earth
100
Hipparchus ( ~190-100 BCE), Star catalog, epicycles
adopted for astronomy, precession discovered and
quantified
0
45 BCE Julius Caesar reforms Calendar, adopt Julian
BCE - calendar ( leap year every fourth year)
>CE
100
200
Ptolemy (100-170CE) 140 Ptolemy's Almagest
300
325 CE Council of Nicea fixes Easter as Sunday
following full moon following vernal equinox
Chinese sunspot
records 28 CE
Water Clocks
Chapter 6 History of Astronomy - History Overview
Medicine Wheels,
Great Plains, Alberta
|
| Teotihuacan
| Empire Mex.
| Nazca culture
| Peru
2A
95
Date
Europe/Egypt/ Modern World
400
500
600
Fall of Rome 473 CE
Church adopts flat Earth, Rectangular heavens above
Middle East/India
700
Al Mansur at Bagdad
gathered astronomers,
Almagest translated
800
Arab Astronomy
Flourishes
@Baghdad,
Tabit ben Korra(836901 CE) translated
Almagest. Noted
difference in
precession between
Ptolemy and current
observations.
Introduced
"trepidation", for
variation in precession
rate
Toledan Tables (made
Toledo, Spain) under
direction of Arzachel,
1080 CE, updated
comptational basis
Hakemite Tables
published at Cairo by
Ibn Yunos
(d 1008 CE)
900
Spherical earth and sky readopted by Church
1000
1100
Euclid/Ptolemy rediscovered in Europe
1200
Albert the Great(1206-1003 CE) &
Thomas Aquinas (1225-1274 CE)- Embrace Aristotle as
authority
Roger Bacon (1214-1294 CE) warns aagainst excessive
reliance on Aristotle
Spain recaptured by
Christians,
Corbova1236 CE and
Seville1248 CE
China
Americas
| Start Mayan |
|
|
| End
|
| Teotihuacan |
\/ Climax of
|
Maya
|
Earliest date for |
Anasazi petroglyphs of
supernova? |
End Maya
\/
Uxmal and other
Yucatan sites
Chinese record Crab Caracol built, Yucatan
Supernova in
Chaco Canyon, N.M.
Taurus
habitation
Chaco Canyon, center
of activity
Bighorn Medicine
Wheel est. (1200 1700)
End of Islamic
astronomy in West
Pope Alfonso X directed Alfonsine Tables 1252 CE
(ellipse for Mercury orbit)
1300
1400
Copernicus (1473-1543 CE)
Chapter 6 History of Astronomy - History Overview
Chaco canyon
abandoned by Anasazi
Aztec Empire, Mexico
3A
96
Date
Europe/Egypt/ Modern World
1500
De Revolutionibus published 1543 CE
Tycho Brahe-1546-1601 CE
Supernova in Casseiopeia 1572 CE
Comet 1577 CE
Observatory at Hven 1576-1597 CE
Middle East/India
China
Americas
Inca Empire, Peru
1519 Cortez conquers
Mexico
1582 Gregorian Calendar adopted in Italy, Spain,
Portugal (Oct 15 followed Oct 5), 12/82 adopted France,
Belgium, Catholic Netherlands.
1583Bavaria and Austria
1584Protestant Belgium, Catholic Switzerland, Bavaria,
Moravia adopted,
1587 Hungary
1600
Johannes Kepler (1571-1630 CE)
Elliptic Orbits, Laws 1609, 1626
also Optics
Galileo (1564-1642 CE)- Telescopic Discoveries 161011,
( sunspots, moons of Jupiter, phases of Venus,
mountains of moon, rings of Saturn,
Star Messenger 1610
Dialogue on Two Principal World Systems 1633
Tried by Church 1633, recanted
Newton (1642-1730 CE)
Optiks,(1704)
Newtonian telescope, light split into colors
Principia 1687 1ST ed, Revised by Newton 1713 and
1826- Includes Computational basis of motion, 3 laws of
motion, Law of Gravity, the Calculus
1700
1675 Greenwich Observatory Founded (goal to make
star catalogue good enough to support longitude
determination from Moon position)
1700 Germany and Denmark adopt Gregorian Calendar
1750 Thomas Wright models galaxy as a lens shape
based on number of stars in various directions
1752 Britain and the Colonies adopt Gregorian Calendar
1772 - Titus - Bode Law, Numerical Relation for semi
major axes of planet orbits
1781 -Herschel discovers Uranus while mapping bright
star positions
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Date
Europe/Egypt/ Modern World
1800
1801 Ceres discovered by Giuseppi Piazzi
1838-Parallax of 61 Cygni discovered by William Bessel
(1784 -1846), first time parallax of a star is found
1846 Neptune discovered by Galle in accord with John
Couch Adams and Leverrier's predictions
1900
1910
1920
Middle East/India
China
Americas
Solar Spectrum observed, Helium discovered
1900 Planck determines that light is radiated in discrete
amounts called photons
1916 Theory of relativity
1917 Russia accepts Gregorian Calendar
1919 Rutherford discovers the proton
1926 Robert Goddard launches first liquid fuel rocked
1927 Heisenberg Uncertainty Principle ( we cannot know
the position and the velocity of a particle arbitrarily well,
no matter what we do)
Expansion of the Universe found ~1928 (Hubble const)
1930
1940
1950
1960
1970
1980
1990
2010
Clyde Tombaugh discovers Pluto 1930
Quantum Mechanics
Atom Bomb (fission)
Distance to Andromeda Galaxy proves it is outside Milky
Way
1948 Hale Observatory at Mt Palomar completed
1949 Gregorian Calendar Adopted, China
Hydrogen Bomb(fusion)
Pulsars and Quasars discovered
First Lunar Explorations, landing 1968
Cosmic Background radiation (3 degree) discovered
Viking Landers reach Mars 1976,
Pioneer probes to Jupiter and Saturn
Voyager leaves for Jupiter Saturn, Uranus, Neptune
COBE satellite measures uniformity of Cosmic
background radiation
Hubble Space Telescope Launched
Chapter 6 History of Astronomy - History Overview
2012 End of Mayan
Great cycle
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Chapter 7 The Start of Modern Physics
Science was not halted by the Church in 1633. The scene moved to northern Europe where the
Pope had less influence. Isaac Newton (1643-1739 CE) was born in Wolstoncroft in England, to a
farm-owning family. Newton’s father died before Newton was born, and his mother remarried.
Newton grew up on their farm, but it became clear that he would not make much of a farmer. He
was sent to Cambridge University at ~18 and stayed for 4 years.
At the end of that time, in 1665, everyone was sent home from the University because the
Bubonic plague was about. The only thing they knew to do to prevent the plague from spreading
was to disperse people. (What does spread the plague? Could you get he plague today?)
Newton went home to the farm, and in the next 18 months figured out the physics you would
study in about 3 semesters at college. He also invented the branch of mathematics, Calculus. He
didn’t write things down immediately, however. He was concerned that someone would steal his
ideas. Only many years later, after urging by Edmund Halley, did Newton document his work in
the books “Principia” and “Optics”. Newton was always afraid that others would try to steal his ideas and take credit for them. When the plague abated, Newton went back to Cambridge, where
his professor resigned to give Newton his job.
Newton determined the following three general laws, which definitely break with Aristotle. They
are applicable to any sort of body.
Newton’s Laws of Motion (these are the only ones called Newton’s laws)
I. In the absence of an outside influence, a body at rest will remain at rest, and a
body in motion will remain in uniform, straight line motion. (do nothing, nothing
happens)
II . Force = Mass x Acceleration
III. For every action that a body exerts on another body, it experiences and equal
and opposite force (action=reaction). (In this context, action means force. So the
law says that the forces of interaction between any two bodies are equal but
opposite)
These laws are very general. They allow numerical predictions of what will happen during
interactions. In a way, all three are restatements of the second law. The first law is the case of the
second law when there is NO force. The third law says that when two things interact, ANY two
things, they both experience the same force, but in opposite directions. It is sort of an accounting
rule.
It often bothers people to think that when a bug hits your car, both the car and the bug experience
force of the same magnitude. It doesn’t mean that the effect on the bug and the car are the same. Which one experiences the greater effect, the bug or the car?
Conservation Laws
Newton and later physicists also figured out several more fundamental laws, called conservation
laws. A conserved quantity in physics is one that is never created or destroyed. This is
nearly the opposite of what we think of in everyday life. Because we can predict the amount of a
conserved quantity, sometimes we can predict what will happen.
One might think of money as a conserved quantity. It does not appear or disappear, it is
transferred from one person or account to another. So it can be worthwhile to hire an accountant
to figure out what you have and where it is going. It is possible to predict how much money you
have left.
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On the other hand, ideas are not conserved. It if you add up the ideas of all the people in the
room, it will not lead to a prediction of the number of ideas in 5 minutes. The conservation laws
are often more useful for predicting what will happen, than are Newton’s laws of motion. Conservation Laws
To use each law, add up the quantity for EVERYTHING involved and get a total before an
interaction. Set the total equal to the total for EVERYTHING after the interaction. All of the laws
are all true all at one time.
Linear Momentum Mass x velocity

(m1beforev1before

m2beforev2before ....)

(m1after v1after

m2 after v2 after
The arrow above v for velocity indicates that its direction matters. The three dots (called
ellipsis) means that there can be more terms
....)
an
Angular Momentum
Mass x Velocity in the direction around the Center x Distance to the Center


(m1beforev1before r1before


m2beforev2before r2before ....)




(m1after v1after r1before m2 after v2 after r2 after
....)
Angular Momentum has a magnitude and a direction associated with it. It is always conserved,
but the law is most useful when there is something obviously going around something else.
Total Energy
(m1beforev12before m2beforev22before ....) (m1after v12after
m2after v22before ....)
The total of all the energy in all the forms is conserved
2
Kinetic Energy
1/2 Mass x Velocity
Potential Energy takes many forms,
All convey the possibility of causing velocity
Gravitational Potential
Calories
Chemical Energy (like in gasoline and cooking gas)
Also, not known to Newton,
2
Rest Mass Energy = Mass x c
Why are there conservation laws? People don’t decide that they should exist, the Universe does.
They indicate symmetries in the structure of the Universe. There may be more conservation laws.
In the laws governing how elementary particles work, there are some conservation laws
governing how one (or more) particles transform into others. These laws are sometimes broken,
so they have a rather different status from the laws above.
What is the use of the conservation laws? They give us some idea of what will happen in physical
situations. Sometimes we know enough about a situation that the specific result of an interaction.
Sometimes we can only rule out some consequences.
HOW TO USE A CONSERVATION LAW
To use a conservation law, we find all the bodies involved in an interaction or situation. Then find
the amount of a conserved quantity associated with each body and add up the amount of each
conserved quantity to find the total BEFORE an interaction. AFTER the interaction, the total will
be unchanged. In situations where we know some, but not all, of the quantities, the conservation
law(s) allow us to find the remaining quantities.
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Example:
You are driving your 1500kg car at 80 km/hr going East and you run head on into a 3000 kg truck.
The truck was going west at 20 km/hr before your collision. After the collision, your car and the
truck stick together. No one puts on the brakes. How fast are you (both) going after the collision?
Answer:
The information given tells the masses of the cars and their velocities. So we know enough to
compute the total momentum before the collision. Adding it up
Total Momentumbefore = m1v 1
m2 v 2
before
(1500kg)(80km/hr) + (3000kg)(-20km/hr)
120,000kg km/hr - 60,000 kg km/hr
60,000 kg km/hr
The truck’s velocity and your velocity have opposite signs because they go opposite directions. The total momentum has a positive sign, because your car had more than the other car. You
made the decision to call eastward positive. It really doesn’t matter which direction is positive, but you need to keep track.
Now we need to figure out the velocity of each vehicle AFTER the collision. We know that if the
two vehicles stuck together, they must be moving with the same velocity. After the collision
TotalMomentum = 60,000kgkm/hr
(1500kg)(v) + (3000kg)(v) = 60,000kgkm/hr
(4500kg)(v) = 60,000kgkm/hr
Dividing both sides by 4500kg yields
60,000kgkm/hr
= v
4500kg
13.3333km/hr= v
Both vehicles are going the same direction at 13.333km/hr. They are both going to the EAST.
You can tell because you set up the problem with Eastward velocity as positive. Since your
answer is positive, it must be East.
What if you had been going the same direction (both eastward) and you rear-ended the truck?
Assume that the two vehicles had the same masses and velocities as before, except you are both
going East. If they stick together after the collision, how fast would you be going after the
collision? (40 km/hr eastward)
Example 2
You are parked behind your friend’s 2000 kg car. Your car has mass 2500kg. You mess up. You put your foot on the accelerator too hard. Then you realize what you have done. You take your
foot off the accelerator, but your car runs into the other car at 4 mph. Your friend’s car is sitting, parked, in neutral. If your car is going 1.5 mph after the collision, how fast is your friend’s car going? Again, we can use conservation of linear momentum. Before the collision
TotalMomentumbefore = m1v 1
m2 v 2
before
(2500kg)(4mi/hr) + (2000kg)(0mi/hr) = 10000kgmi/hr
After the collision, the total momentum is the same, and the velocity of your friend’s car is unknown, so
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(2500kg)(1.5mi/hr) + (2000kg)(v) = 10000kgmi/hr
3750kgmi/hr
+ (2000kg)(v) = 10000kgmi/hr
(2000kg)(v) = 10000kgmi/hr - 3750kgmi/hr
= 6250kgmi/hr
v = 3.125 mi/hr
We know that your friend’s car is going in the same direction that your car was going because the answer has the same positive sign as your original motion had.
The law of conservation of linear momentum is generally useful. It is equivalent to Newton’s second law, but is easier to use, because we scarcely ever know the exact force between two
bodies at every instant. Conservation of linear momentum adds up all the effects of the forces
and allows us to know the situation after the interaction.
The law of conservation of angular momentum is always true (and it is possible to define the
radius to any center you like), but it is most useful when something is obviously going around
something else.
Conservation of energy is always true as well, but there are many formulae for the potential
energy. It is often more useful as a general concept. For example, in the car-truck collision, the
kinetic energy of motion of the vehicles is transformed into potential energy by crunching the
metal. The amount of energy used in bumper crunching depends on how the cars are built.
Gravity
Newton also discovered the force of gravity. The story is that he was thinking about why the
Moon orbits the Earth and what keeps it from getting away. Then an apple fell. He realized that a
force between every object and every other one must exist, and that the form of the force law is
The negative sign in the force law
indicates that the force is in the
direction to pull the bodies
together, the force acts along the
line joining the bodies.
Gm1m2
F
r2
F the force
G = the Universal Constant of Gravity According to Newton, there is a
force of gravity between every pair
m1,m2 the two masses involved
of bodies. Or better, between
two particles with mass.
There is no minimum size of the and there is no maximum distance for gravity to act, so far as we
know. So you are pulling on and being pulled on by galaxies you have never seen; ones you
didn’t know existed. So why don’t we feel the gravitational force from each other?
r = the distance between the masses every
The value of G, the Universal Constant of Gravity, is a small number. So the force between you
and me is very small. On the other hand,
gravity always attracts. So it builds up to a
large value between big bodies like planets
and satellites.
m
m
m
Mt
m
All parts of Ea rth
pull on the obse rv e r
The distance s and
amounts of mass av e rage to
act like all mass at the ce nte r
Chapter 7 The Start of Modern Physics
As we consider the force of gravity from
some large body, it becomes obvious that
the material is not all at the same distance.
To find the total force of gravity between
two bodies, one would add up the forces
between every tiny piece of each. This gets
old really fast.
4
102
So how did Newton compute the force between the Earth and Moon? Newton, used the Calculus
(mathematics,not the tooth scum) to add up the force from the different particles in a large body.
One of the things he proved was that
The force from a body with spherical symmetry produces the same gravitational force as
would the same total mass concentrated all at the center.
So when we compute the force of gravity on an object on the surface of the Earth, the
distance between the body and the Earth is the radius of the Earth.
Example:You weigh 150lb on the surface of the Earth.
How much would you weigh on a tower 1 Earth radius high?
The 150lb is NOT your mass; it is your weight, the force of
gravity between you and the Earth. Your bathroom scale is
squashed because of this force. The very idea that the weight
changes indicates that 150lb is not your mass.
It is possible to use the force to figure out your mass, but it is
not necessary for solving this problem. In stead, we can solve
the problem by comparing the situation at the lower and the
higher positions. This method simplifies the computation,
Bathroom Scale
2Re
Start by writing out the force of gravity on you standing on the
Earth.
Gm1m2
r2
The general law is Fg
Re
.
Substituting the variables for this specific case (just the names, not the numbers).
150lb
Gmearth myou
Rearth
2
Now set up the equation when at the top of the building, at a distance of 2R earthfrom the center of
the Earth.
Fg
Gmearth myou
2R earth
2
Gmearth myou
Gmearth myou
(2)2 (R earth )2
4R earth
2
You still don’t know your mass, but the right hand side has all the same terms as the force of
gravity on you on the Earth. So, factoring out the parts that equal your weight produces
Fg
Gmearth myou
4Rearth
1
150lb
4
2
1
4
Gmearth myou
Rearth
2
37.5lb
2
So doubling the distance from the center of the Earth, divides the force of gravity by 2 , or 4, and
it was not necessary to know your mass, or the Earth’s mass or the constant of gravity.
Test Yourself: Your dog really wants to be picked up, but at 110lb he is too heavy. You get the
idea to take the dog to the top of a tower 1.5 Earth radii high, then lift him. Will this help? How
much will he weigh at the top of the tower?
Ans 17.6lb
What if you want to go to Mars with your dog? What will the dog weigh? In this case BOTH the
mass of the planet and the radius of the planet change. The mass of Mars is about 0.107 x mass
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of the Earth and the radius is about 0.53 of the Earth’s mass. The dog’s mass doesn’t change. Fg
Gmdog mmars
Rmars
2
Gmdog 0.107mearth
(0.53Rearth )2
You finish the computation. The dog will
weigh 0.381 x as much as on Earth’s surface = 41.9 lb
Circular
and
Escape
Velocity
Newton discovered gravity
because he was thinking
about why the Moon orbits
the Earth. As he worked out
the problem, he discovered
that an orbit would be a
circle, an ellipse, a parabola
or a hyperbola. These
shapes are shown in the
figure.
Newton found that for an
object, m1 to go in a circle
around another object, m2,
a body must have exactly
circular velocity compared
to inertial space.
The
circular velocity formula is
Vcirc
Starting Point
HYPERBOLA
F
D
G
E
H
ELLIPSE
C
A
B
CIRCLE
PARABOLA
ELLIPSE
Gm other
r
For one body to escape from another, it must have escape velocity.
Escape Velocity Vesc
2Gm other
r
2 Vcirc
When one body escapes from another, it has just enough velocity so that gravity slows it down
forever and it finally gets to zero velocity at an infinite distance. But it is never pulled back.
Again this is the speed of mass 1 compared to inertial space, not to mass 2
Newton didn’t know the value of G. On the other hand, the velocity of the Moon is easily found from the distance to the Moon and the time for the Moon to complete its orbit.
To orbit the Earth at about 100 miles altitude (but r~ 6400 km, since it is measured from the
center of the Earth) requires a speed of about 7.8 km/sec. The Moon, on the other hand is nearly
400, 000 km away and its speed is much less, approximately 1 km/sec.
Does this make sense? The gravity force pulls one body toward another. The crosswise motion of
the objects (compared to one another) keeps them from just falling into one another. Since gravity
is smaller at greater distances, the crosswise velocity needed to prevent impact is smaller.
The speed of the Earth as it orbits the Sun is about 30 km/sec. It is nearly constant, since the
distance to the Sun is nearly constant. For the Earth to escape from the Sun, we would need to
give the Earth only 2 times as large a velocity, or 42.3km/sec. That is just an extra 12.3 km/sec.
If an object has speed greater than escape velocity, it moves on a path called a hyperbola. It will
be able to escape from the other object. It will slow down until its speed is the difference between
its original speed and the escape velocity.
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Example
How fast does an asteroid at 4 AU orbit the Sun (assuming that it is orbiting in a circle)?
The formula we use is the formula for the circular velocity,
Vcirc
Gm 2
r
In this case, the
Sun is m2 and the distance between the centers of the Sun and the asteroid is 4AU.
It is possible to look up G, Msun and then to convert 4 AU into meters. So in this case, it is
possible to plug all the values into the equation for circular velocity, convert units and find out the
speed. This is fun ONE time, but there is a faster way.
Since we already know the velocity of the Earth as it orbits the Sun, and the distance to the Sun,
and the fact that the Earth is much less massive than the Sun, the following can be done.
First write out the circular velocity law and plug in the definitions for the Earth in orbit around the
Sun.
Gm sun
1AU
and substituti ng the answer is
Vearth orbiting Sun
G(m sun )
1AU
30km/sec
Write
the
equation
Vcircular, asteroid orbiting Sun
for
the
velocity
of
the
asteroid
orbiting
the
Sun
at
4AU
Gm sun
4AU
Factoring the equation for the asteroid’s velocity to isolate the terms that appear in the formula for
the velocity of the Earth produces
Vasteroid orbiting Sun
G(msun )
4AU
1 G(msun )
4
1AU
The term in the square root sign is something you have seen before. It is just the formula for the
circular velocity of the Earth. But we know the answer, that is, the value of the Earth’s orbital veloicity. So substituting for the Earth’s orbital velocity yields
Va ste roid orbiting Sun
1 G(m sun )
4
1AU
1
V
4 e arth orbiting Sun
1
30 km/sec
4
1
30 km/sec = 15 km/sec
2
What was the point? Since one result was known, we didn’t have to do any complicated computations. Please notice, the asteroid is 4 times as far from the Sun as is the Earth, but the
speed in orbit is half as large. The speed does fulfill our precept of “ faster when closer”, but the speeds are not proportional to the distance. The speed varies less strongly.
Test yourself. How fast does Pluto go in its orbit? (The answer is in the book, but be certain that
you can compute the answer).
How fast would we need to make the asteroid go to get it to escape from the Sun? The asteroid
would need to go √2 xVcircular, or √2 x 15km/sec = 21.2132km/sec or faster
How fast do we need to escape from the Earth? Remember that you already know how fast a
body would need to go to orbit the Earth near its surface.
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The formula for escape velocity is found based on the idea one body escaping from another with
nothing else around. In real life, there are always other objects and the effect of their gravity must
be considered as well.
Can we always escape? We, you and I, don’t personally have the velocity. That is what we build
rockets for. But even with the best conceivable rocket, escape is not always possible.
We think that the fastest anything can go is c, the speed of light, 300,000km/sec. So what if the
escape velocity
Ve sc
2Gm
equals or exceeds the speed of light? Then we think that nothing
r
can escape and we term the situation a “black hole”. The place where the escape velocity
equals the velocity of light. This is called the event horizon.
When we are far away from a black hole, we experience normal gravity. We are not sucked in. If
you get near the region where the escape velocity reaches the speed of light, eventually an
orbiting body will spiral in. If something crosses the event horizon, it cannot escape and no signal
from it can come out.
You might imagine the black hole like the toilet. It isn’t at all dangerous from far away, but once you get too far into the bowl, too bad.
Black holes can come in any size. We have already discovered black holes which appear to be
the remains of a massive star. The part that is left has perhaps 7 times the mass of the Sun.
These black holes are detected by the fact that they are in a system with another star and the
other star orbits the black hole (far enough away that it is not sucked in).
Another type of black hole we have discovered lives at the centers of galaxies. In this case the
black holes have millions to billions of times the mass of our Sun. We are not certain how they got
the mass, but probably they have been swallowing stars for billions of years. The center of our
own Milky Way includes such a black hole. Larger galaxies have more massive black holes.
How can we find a black hole anyway if nothing comes out of it?
Basically we need to observe something nearby. If there is something orbiting the hole under the
influence of its gravity (but not already sucked in), we can use the circular velocity law to find the
mass in the hole. Remembering that Vcirc
Gm 2
, we would observe the velocity, Vcirc, and
r
the distance between the bodies, r. It is not really necessary to see both bodies, since the size of
the orbit can be seen from the motion of just one, The value of G is known. So everything is
known except m2. So we solve for the sum of the mass of the other object. If the mass is large
and there is no luminous body visible, it is possible to infer that there is a black hole.
This method, measuring Vcirc and r, and using the circular velocity law to find the mass, is the way
we measure the mass of all celestial bodies. If the laws of physics or G are different elsewhere or
at other times, we have the wrong values for masses of most celestial objects.
Practice Problems
1) How far would you have to go to feel no force from the Earth's gravity?
2) You hit two different golf balls off the tee. You hit both exactly the same, but one has twice the
mass of the other. Which leaves the tee faster? What law (s) of physics are useful here?
3) You are throwing a dodge ball against a grocery cart. The dodge ball bounces back to you.
What will the cart do? What law (s) of physics are helpful for finding the answer?
4) When you throw a ball in the air, it comes to a halt and returns. What is the kinetic energy at
the highest point of the ball's trajectory? Is this the same kinetic energy as when the ball leaves
your hand? If not, what happened to the energy?
5) You buy a 5 lb sack of rice at sea level, what does it weigh on top of a tower 3 earth radii high?
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Answers 1)There is no place you can go 2) The one with twice the mass leaves with half the
velocity. Use Newton's second law 3) Grocery cart moves away from you, conservation of
momentum or Newton's 1st and 2nd laws 4) 0 at the top of the trajectory, it became potential
energy 5) 0.3125lb
Using Equations and Formulae
Many students ask, “How do you know what equation to use and how do you know what to do with it?” While we don’t know what to do in every situation, it is often easy to decide which formulae to use.
As we look at the laws and formulae in this course so far, they can be organized as follows:
Kepler’s 3 laws
Newton’s 3 laws of motion
Three conservation laws
Three formulae concerning motion with gravity
In the future, we will learn another formula concerning the Doppler shift of light
Each of these laws concerns a specific subject and involves just a few variables. The first step to
knowing what to use is to understand the topic (s) of the formulae and to know what the variables
stand for. Once you know the topic, you can be the judge of when to use the information. For
example, if your car won’t start, you look for a car manual, not for instructions on how to substitute cooking oil for butter in cookies or how to reboot your home computer. Then you look in
the instructions or the topics and look for the ones that say “car doesn’t start”, not ones to help change a flat tire. Then you start looking at the symptoms, like “key doesn’t turn” or “key turns but doesn’t cause the motor to rev” etc. When you find whatever looks the closest to what you have, you try what the book suggests.
Hopefully, this sounds like basic common sense. It is, just use yours.
So the steps are to first
1) Decide the topic of the law or equation
2) Know what all the variables are and what they mean
These steps should be done as you learn the equation. They don’t depend on the problem at hand. The table on the next few pages has spaces for you to fill in the laws, their topics and
variables. Leave the Doppler shift equation until after you have studied it. But do fill in the others.
So first of all, let’s break out the equations and identify what the topics are. Remember, the laws
and definitions are in the chapters.
So, check yourself.
a) What topic is Kepler’s third law about? b) When would you use Newton’s third law?
c) What is the G in some of the equations?
d) Where is r, the distance between bodies measured?
e) What can you do with Kepler’s first law? What can be computed?
So now how would you use the equations or laws? All of them are true at the same time, but they
don’t always relate to the issue at hand. So look for the one or ones that matter.
Which law or laws are relevant for the following situations?
f)
How much does a 2 lb package of meat weigh when it is on top of a mountain 0.55 Earth
radii tall (above sea level)?
g) If you notice a comet orbiting at an average distance of 35 AU from the Sun, how long will
the comet take to complete an orbit?
h) How fast must the comet from the question above go?
i) How fast would the comet from the question above need to go to escape from the Sun?
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j)
A comet goes from a distance of 10 AU from the Sun at the closest to a distance of 50
AU at the furthest. Where does it move the fastest?
k) A comet goes from a distance of 10 AU from the Sun at the closest to a distance of 50
AU at the furthest. Where does it experience the most force from the Sun?
l) You are shooting arrows with a bow. You always draw the bow the same amount and the
bow doesn’t age etc. If you have some arrows that are more massive and others that are less massive, how can you tell which is which?
m) With the bow and arrow above, the arrow should have energy after it leaves the bow.
What kind of energy did it get? Where did the energy come from ?
n) If the bow from the previous question puts a force of 30 lb on the arrow, how much force
does it put on the person holding the bow?
o) You rear end another car while you are going straight East. Your car has a mass of 1500
kg and the other has mass 1200kg. You were going 10 m/s before the accident and the
other car was going 8 m/s to the East before the collision. Can the other car go to the
North as a consequence of the collision?
p) If you are going 9 m/s after the collision from the question above, how fast is the other car
going?
q) Is there any body damage in the car accident above?
r) How much will you weigh on a planet with half the mass of the Earth and half the radius?
Hint: compare your new weight to your weight on Earth.
s) You hit a golf ball and give it some spin. You are at a golf practice range which is very
noisy and small. So you cannot hear when you hit a ball. You are a good golfer and every
ball hits a net at the end of a short practice area. If you hit every golf ball the same, is
there any way to tell whether the ball is a hollow practice ball or a ball with a rubber
interior?
t) Consider the golf ball from the problem above. The cover of the ball opens and the
wrapped rubber band inside starts to unravel, will it spin faster or slower than before it
started to unravel?
Once you have decided which law is relevant, then it MAY be possible to find a numerical
answer. There are several issues to remember, however.
First, some of the laws don’t give a numerical answer. Which ones? Kepler’s first law doesn’t. Kepler’s second law can, but the computation is beyond what we are going to learn. The law of conservation of energy also doesn’t give easy numerical values.
Second, some of the laws, like the law of gravity, the equations for circular and escape velocity
2
3
and Kepler’s third law (P = a ) have equations with answers that deal with one situation.
Others, like conservation laws need values BEFORE and AFTER an interaction. So look for that
before and after situation to know if you might used conservation
Example: You live on the planet Zonds. You wake up this morning and weigh 200 lb. The planet
is having a really bad day. Over the course of the day, Zond swells(due to an excess of
underground gas). Before any of the gas escapes, the surface has swollen until it is 15% larger
than before. You step onto your bathroom scale before leaving for safer locations. What do you
weigh?
Work: The equation to use is clearly the formula for the force of gravity
F
-Gm1m2
, since
r2
weight is a measure of the force between the two bodies. But you don’t know any of the numbers except, possibly G. To plug in and evaluate the force, would be impossible. On the other hand,
we do know the force of gravity, F, to be 200lb to start and we know all the definitions. So it is
easy to make a ratio. The masses are the mass of you and the mass of Zonds. Neither is in any
textbook. The distance, r, is the distance between you and the center of Zonds. It is rzonds at the
start of the day and 1.15 rzonds, 15% larger at the end. So we know:
Chapter 7 The Start of Modern Physics
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108
F
-Gm1m2
r2
start o f the day
200lb
end of the da y
x
-Gmyou mZonds
2
rzonds
-Gmyou mZonds
2
(1 .15rzonds )
where x will be your weight at the end of the day after the planet has swelled up.
The problem tells you that both you and the planet have the same mass as at the start of the day.
Expanding the square in the denominator produces
x
x
-Gmyou mZonds
2
1.3225rzonds
200lb
151.23lb
1.3225
To get to the last step, it we substituted 200lb for all the terms in the formula that produced the
200lb. There was no way to do all the substitutions one by one, because we didn’t know the individual values.
In the problem above, it was clear that it would be necessary to use the force of gravity equation.
What about using a conservation law?
For example: You are playing croquet with an odd set of balls. You hit your ball and give it a 1m/s
going north. It hits a stationary ball which has twice the mass of yours and stops immediately.
How fast does the other ball going after the collision?
Answer: Look at the equations and the information you have. You can decide by process of
elimination. The information has no data concerning force. So Newton’s laws of motion aren’t useful. The motion of the croquet balls isn’t determined by gravity. Gravity only keeps the balls on the ground. Kepler’s laws are related to motion of planets. So that lets out the law of gravity and the formulae for circular and escape velocity. The conservation laws all apply, but the
information is only enough for the conservation of linear momentum. So to use a conservation
law:
Find the conserved quantity, the total linear momemtum, before the interaction.
Mass of your ball x velocity of your ball +Mass of other ball x velocity of other ball =
(M)(1m/s) + (2M)(0)=1Mm/s
Total linear momentum after the interaction
Mass of your ball x velocity of your ball +Mass of other ball x velocity of other ball =
(M)(0m/s) + (2M)(x)= the total momentum from before the balls hit, that is =1Mm/s
2Mx=1Mm/s
x=1/2 m/s
There is enough information to solve for the final situation, after computing the
total momentum and ignoring the fact that we don’t know the mass of our croquet ball.
Give the problems a try. First do a – e, then look at the rest and see what law to use.
Answers follow the table.
Chapter 7 The Start of Modern Physics
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109
Name of Law
1
Kepler’s First Law
2
Kepler’s Second Law
3
Kepler’s Third Law
4
Newton’s First Law of Motion
5
Newton’s Second Law of Motion
6
Newton’s Third Law of Motion
7
Conservation of
Linear
Momentum
Chapter 7 The Start of Modern Physics
Statement of Law Topics
or Formula
Definitions of the Variables
12
110
8
Conservation of
Angular
Momentum
9
Conservation of
Energy
10 Law of Gravity
11 Circular Velocity
Equation
12 Escape Velocity
The following
coming
is
Doppler Shift
Equation
Chapter 7 The Start of Modern Physics
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111
Ans Here you are deciding what law to use. a) The relationship between the period, P, the time to
orbit the Sun, and the distance from the Sun as represented by the semimajor axis of the orbit, a
b) When you have an interaction between two bodies. It doesn’t tell how large the force is, but -11
does say both bodies feel equal force c) The Universal Gravitational Constant, 6.67x10
3
2
-1
m /(s kg ). But you won’t need to know the value. d) r is the distance between the bodies
producing force in the formula. It is measured from the position of the actual mass involved. In the
case of spherically symmetric bodies, the effective distance of each body is at the center. e) You
can decide whether a path is an ellipse and is or isn’t a proper path for a planet, or other body, orbiting due to gravity. You can’t compute anything with it easily. f) force of gravity g) Keplers third law h)Circular Velocity Equation i) Escape Velocity Equation j)Kepler’s second law k) force of gravity l) Newton’s second law m) Conservation of Energy n)Newton’s Third Law o) Conservation of Linear Momentum p) Conservation of Linear Momentum q) Conservation of
Energy, there is less kinetic energy after the collision, so some energy must have gone to
potential, in the form or crunching the metal of the cars. r) force of gravity s) Newton’s second law t) Conservation of Angular momentum
Now try to get numerical answers
Ans the numerical values f) 0.832lb g) 207.1 years h) remember that the Earth orbits at 1 AU and
has a speed of 30 km/sec. Then use the circular velocity equation and take the ratio of the
velocities for the two distances 1 AU and 35 AU. to get 5.07 km/s. i) (√2)circular velocity =(√2)5.07km/s=7.17 km/s j) When it is closest to the sun, at 10 AU. You haven’t learned any formula for this specific speed and I am not expecting you to. But the essence of the law is
conservation of angular momentum, so there are ways to figure out the speed if you feel so
inclined. k) When it is closest, because of the law of gravity. Since we don’t know the mass of the comet, we cannot compute the force. l) The more massive arrow accelerates less due to the
force from the bow which is the same on all different arrows. Since it accelerates less, it goes
2
slower when it leaves the bow entirely m) The arrow gets kinetic energy, 1/2 mv , from the bow.
The bow has potential energy stored in the stretched string. The bow also must get a little kinetic
energy after the arrow leaves, because of conservation of linear momentum. There was zero
velocity for the bow and for the arrow before the arrow went free. After the arrow is released, it
has momentum in one direction. The bow must have equal and opposite momentum in the other
direction to fulfill the conservation law. n) 30lb, but in the opposite direction, as Newton’s third law states o) No, momentum must be conserved. Before the collision, all the momentum was
eastward, and your car has all the momentum. After the collision, all the momentum must be
east. Your car has ONLY eastward momentum and its momentum is less than before the
accident. So it cannot cancel any northward momentum from the other car. Thus the other car
can have only eastward momentum. [) 9.25m/s, by conservation of momentum q) Yes, but you
can’t tell how much. You can tell that there is SOME body damage by checking out the kinetic
energy of the system before and after the collision. There is slightly less kinetic energy in the two
cars after the collision than before. Since the total of kinetic and potential energy is conserved,
there must have been a change in the amount of potential energy. It would go into squashing the
cars. r) Make the ratio of the force between you and the Earth F
Gm you mearth
2
rearth
your weight
and the force between you and the other planet is
F
Gmyou mplanet
2
planet
r
1
Gmyou
m
ear th
2
1 2
4 ear th
r
2
Gmyou mear th
2
rear
th
Gmyou
1
1
2
mear th
( 2 rear th )2
your weight on new plan et
your weight on new plan et
your weight on new plan et
2 weight on earth your weight on new plan et
s) The less massive ball, the hollow one, goes faster t) As the ball unravels the spinning material
goes from being closer to the center of the ball to being further. Conservation of angular
momentum says the ball must spin slower because the radius is larger.
Chapter 7
The Start of Modern Physics
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112
Chapter 8 Illuminating Light
Humans are largely earthbound. To date we have stood only on the Earth and the Moon. We
have landed spacecraft on the Moon, Triton, Venus and Mars and have parachuted a probe into
the upper layers of Jupiter. We have flown by all the planets except Pluto and have orbited
Mercury, Venus, Jupiter and Saturn. We get some samples from the Solar Wind and from
meteorites. So how is it that we have the gall to say that we know anything about what planets
and stars are made of? Are astronomers just making it up?
Many people think that if an idea is called a "theory" it is one among many equally good notions.
In science, many ideas called theories are supported by a large interlocking web of evidence. If a
different underlying idea is proposed, it must be consistent with all the known data. Alternate
concepts need to address the evidence and be successful in explaining it.
It does happen that there is more than one explanation consistent with the observations, as we
saw for the geocentric and heliocentric models of the universe. But eventually the data may
distinguish between the models (as happened when the phases of Venus and the parallax of
stars was finally observed).
Astronomers are not just spouting off randomly when they describe conditions at places we have
not been. They are using the laws of physics and observations.
Light consists of a combination of an electric field and a magnetic field changing strength and
direction and moving through space. The structure of light is particularly simple because it
always has the layout shown below.
Wavelength
Electric Field
Magnetic Field
Light moves at c, speed of light, 300,000 km/sec in a vacuum
The electric and magnetic fields are at right angles. They are usually at their maxima at the same
place. There is no particular direction for the electric field. Since one field creates the other, there
is no such thing as just an oscillating electric field moving through space at c without the magnetic
field.
The major feature of light is the wavelength. It tells how long between repeats of the wave. The
figure shows the wavelength between peaks of the electric field. But there is nothing special
about any part of the wave. The wavelength is the distance between the repeats, however they
are arranged.
Light goes at a fixed speed through a vacuum. The speed is called c, and the numerical value is
300,000 km/sec (This is the same as 186,000 miles/second, but we will be using the metric
system). It doesn't matter whether you are moving, light, from whatever source moves at c with
respect to you.
Because light has a fixed speed, one can characterize it by either the wavelength, or by the
frequency, the number of waves passing a point every second. If you know one, you know the
other because
(length of each wave) x (number of waves passing each second) = speed of wave packet
Hopefully this word equation is no surprise. The speed is always the same, c, 300,000 km/sec.
So if you know the wavelength, the frequency can be found and conversely.
Different wavelengths cause different physiological responses in us. When light has a wavelength
-7
-7
between 4x10 and 7 x 10 meters or 4000 and 7000 Ångstrom units, we can see light and the
-9
different wavelengths appear as different colors (a nanometer is 10 meters). Other wavelengths
Chapter 8 Illuminating Light
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113
usually cannot be sensed, but do have effects. The figure below shows some of the names for
wavelengths of light.
All of these names refer to the very same set up, crossed electric and magnetic fields moving
through space at the speed c. The names arose because different wavelengths are detected
differently. While all these names are given to different wavelengths of light, there are a couple of
similarly named things that are NOT light. Sound is a vibration of material, not a form of light.
Cosmic rays are particles from outer space. Radiation is a general term that includes light, but
also includes particles given off from radioactive elements,
Light comes in individual packets called photons. When light is brighter, there are MORE
photons, not photons with higher waves. The shorter the wavelength, the more energy carried by
each photon.
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There is a variety of ways to cause light. A changing electric field can generate light. This is the
way that radio stations form their over-the-air signal. Their antennas are visible near SF Bay on
the mud flats. They are just straight, vertical antennas about 1/4 wavelength. Electrons,
negatively charged particles, are sent up and down the antenna. Each charge carries and electric
field. The electron’s motion causes a varying electric field. The electric field causes the magnetic
field. And the combination is a form of light. The resultant radiation is what you pick up on a radio
receiver. The sound you hear is the result of the signal being used to vibrate a mechanical piece,
often made of paper.
In astronomy we are very concerned with light made by atoms and molecules because it allows
us to find out about the source. To understand the way it works requires that we learn about
atoms and molecules.
Atoms all have a nucleus with positively charged particles called protons and neutral (no charge)
particles called neutrons. Almost all of the mass of the atom is in the nucleus, although the
nucleus takes up about 1/100,000 of the radius of the atom. The number of protons determines
the type of atom, that is what element it is. Each element can have a various numbers of
neutrons. The number of neutrons determines the isotope (of the element).
As you may have heard electric charge comes in both positive and negative and opposites
attract, like in love. The closer together, the stronger the attraction or repulsion. The attraction
keeps negatively charged particles in orbits as close to the nucleus as physics allows. The reason
that protons in the nucleus stay together (in spite of the their electric repulsion) is that there is
another, stronger force, called the strong force acting on the protons and neutrons. The strong
force is much stronger than the electrical repulsion at small distances. The strong force gets
much smaller than the electrical force at large distances.
Negatively charged particles, called electrons move around the nucleus in paths or areas
orbitals. These orbitals have a variety of sizes and shapes. Each orbital can be occupied by up to
a specific number of electrons. "Normally" the number of electrons is the same as the number of
protons, so all the charges cancel. If the number of electrons is NOT the same, the situation is
called an ion.
All of chemistry, all of the processes that usually occur on earth are changes in how the electrons
from one or more atoms are shared. The nucleus of the atom is not normally affected.
Electric force pulls the electrons toward the nucleus. Electrons have kinetic energy that keeps
them from falling into the nucleus. This is rather like the case with planets orbiting the Sun.
Gravity pulls the planets, their kinetic energies keep them from falling in. If we want to move
electrons to orbits further away from the nucleus, energy needs to be added.
Unlike the orbits of the planets, the electrons cannot go to just any path around the nucleus. Each
type of atom, molecule and ion has a unique set of orbitals corresponding to the possible energy
levels. These orbitals have no physical presence when no electron is in them, but they define the
only paths the electrons can take.
Chapter 8 Illuminating Light
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115
Energy Levels
Available to electron
Nucleus
-e
+p
Energy Levels
get closer
together in both
energy and space
going further
from the nucleus
Electrons have a lowest energy
level, typically the orbital allowing
the electron to be closest to the
nucleus (compatible with the
positions of other electrons). When
an electron is in any but the lowest
energy level, it will eventually return
to the lowest level. As it does this,
the excess energy is released.
Typically a photon with just the
right energy is given off to get rid of
the energy.
When a sample of a material has
its electrons excited, different
electrons go into different levels. As
the electrons come back to lower
energy levels, the pattern of
wavelengths (colors of light) allows us to distinguish the type of atom or molecule. It is rather like
the fingerprint of the material.
The pattern of bright light from a diffuse gas is called an emission spectrum. It consists of bright
light at the wavelengths (energies) corresponding to the transitions to lower energy levels.
Hydrogen light gives a pattern of Red, Teal, and many purple photons when it s electrons jump to
lower energy levels. Mercury vapor gives Purple, Green and brownish-yellow. Atoms also give
light in many wavelengths we cannot see with our eyes. For us to be able to see these colors,
the material must not be too dense and the light from the material must not be overwhelmed by
radiation from the background,
Electrons can be given energy by collisions, by subjecting them to an electric field to counteract
the attraction of the nucleus or by letting them absorb light.
The random motions of atoms result in collisions. The hotter a material, the faster its particles
move and the
more
energy
transferred in a
collision.
(Absolute zero is
the temperature
where
particles
have
as
little
motion
as
possible.) If the
collision causes
an electron to
move to a higher
level, the electron
emits light as it
returns to a lower
level.
If the material is
dense
enough
(like most solids
and liquids and
some dense gasses), the electrons drop from the higher levels to lower levels, but they do not
succeed in giving off exactly the characteristic energy. Collisions from other materials change the
Chapter 8 Illuminating Light
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energy slightly. Many molecules have a great number of energy levels, so a small change in
these levels smears them together. This makes a continuous spectrum.
A continuous spectrum includes all colors including wavelengths not visible to our eyes. The
density obscures the information about the type of material, but it does allow us to tell the
temperature of the material. The distribution of particle velocities, determined by temperature,
determines the amount and the distribution of energy given by a body. Black body spectrum is
the name given to the distribution of energy given by a sample of dense material where collisions
cause the excitation.
The curves below show the amount of radiation a black body gives at each wavelength. The
curves are for bodies of the same size and at the same distance from the observer. A formula
gives the shape of the curve. Astronomers observe the light from a distant body, and compare the
distribution of energy or the peak of the energy distribution to the theoretical curves. Matching the
curve and the observations tells the temperature of the body, In many cases, a comparison of the
amount of light at only two wavelengths is enough to find the temperature. There is also a formula
relating the total amount of energy per second to the temperature for a body of known size. This
formula can be used to find the total amount of energy given by a body.
Ideally a black body absorbs any incoming light equally well and emits any wavelength with no
impediment. Realistically, the overall black body distribution can be used to tell the temperature of
most bodies without too much difficulty.
When an atom encounters light, it can absorb the light if the light is at just the right energy to raise
the electron to a higher energy level. It is not all right for the light to have more energy than is
needed to change the energy level. The electron cannot absorb just part of the energy. It can only
accept light with exactly correct energy. After an atom absorbs energy and goes to a higher
Chapter 8 Illuminating Light
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117
energy level, it eventually returns to the lower energy level, emitting light. The sequence of events
is shown below.
Notice that the electron in the figure above has jumped up TWO levels, rather than one. This is
perfectly all right, if the light has enough energy (and some other relationships between the levels
are met). The electron need not come down to the original lowest level all at once. It could come
to the second level, emitted a photon, and then come down to the lowest level, emitting another
photon.
The direction of the outgoing light is usually independent of the direction of the incoming light. If
there is a bright continuous background (a rainbow), with diffuse (not dense) gas in front of it,
there is a decrease in the amount of light received at those wavelengths absorbed by the gas.
The appearance of the spectrum becomes a rainbow with dark lines where the gas would
normally produce bright colors. This is called an absorption spectrum. The dark lines tell the
same information that the bright lines would. The continuous background can be used to find the
temperature of the background material.
Summarizing the types of spectra:
A continuous spectrum is produced by dense bodies. The distribution of amount of energy
at different wavelengths tells the temperature. The appearance of the spectrum is like a
rainbow, all colors with varying amounts of different colors.
Diffuse material with nothing bright behind it produces an emission spectrum, that is light
at only those wavelengths specific to the material. The type of material can be found from
the pattern of lines produced. The temperature of the material can usually be told from the
distribution of lines and their intensity, but this requires a simulation of the gas.
An absorption spectrum results when diffuse material is viewed with a bright, continuous
source of light behind it appears as though it was in silhouette. The continuous spectrum
appears and dark lines appear at the wavelengths where the diffuse material is absorbing
and reemitting light. The appearance is a rainbow with dark lines on top of it. It is called an
absorption spectrum. The continuous background can be used to find the temperature of
the material in the background. The absorption lines tell the same information as the
emission spectrum would.
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All the colors of the rainbow, one
blends into the next with no
breaks
All the colors cut by
dark lines
Colored lines on dark
background
NOT all colors
Among the things we can tell from light, is how fast we and the source are moving toward or away
from one another. This motion causes Doppler Effect is a change of the wavelength of light.
Doppler effect also occurs for sound, and you have probably heard the change in pitch as a siren
or a race car goes by you.
The reason that Doppler shift occurs is that the distance between the observer and the light
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changes during the time that the light wave is being emitted. When the source approaches, the
wavelength you get is smaller than the wavelength originally emitted. This is called blue shift.
When the source recedes, the wavelength we get is longer and the effect is called red shift,
regardless of the actual color involved. The formula relating the velocity to the Doppler effect is as
follows.
V is the velocity of the body relative to the observer (+receding, - approaching)
c is the speed of light, 300,000 km/sec
λ is the symbol for the ORIGINA:L wavelength of the light, the wavelength sent
Δλ is the change in the wavelength from when it left the source to when it was
received. It is found by subtracting the original wavelength from the wavelength you receive. The
combination Δλ does not mean to multiply, it is like a compound word.
If we have no idea what the original wavelength of the light was, it is not generally possible to find
the velocity of the source. We assume, however, that the spectra of elements and compounds
are the same everywhere. When there is a Doppler shift, all the light from the source is affected.
The pattern of lines will be shifted in a predictable way. So the pattern will still be recognizable.
So if we see the pattern from hydrogen, for example, the red, teal and purple lines would all have
their wavelengths changed by Doppler effect, but the pattern still tells that it is from hydrogen.
Example: You receive the teal line from Hydrogen. It is normally emitted at 4861Å, but you
receive it at 4859 Å. What is the velocity of the source with respect to you?
Write the original equation, then substitute for each variable. The original wavelength is 4861Å
and the change is -2 Å , since what you receive is 2 Å less than what was sent. The speed of
light is always the same, 300,000km/sec. So the Doppler Shift equation is
Substituting
The Angstrom units cancel. Multiply both sides by 300,000km/sec to get
The negative sign indicates that source and recipient are approaching one another. It is not
possible to tell whether one or both are moving.
An effect like the Doppler shift is the way that we found out the universe is expanding. We talk
about the red shift of distant galaxies. Sometimes you will hear the value of the red shift on the
news. The way that it would be said is "Distant galaxy with redshift 6 has been found. The value 6
refers to
Actually galaxies with redshift nearly 7 have already been found. How can that be? The variable z
is the same as the right hand side of the equation for V/c. Does it mean that the speed of the
source is greater than c, the speed of light? Actually no. There is a more correct equation for the
correspondence between shift and velocity. This other equation is
This is the formula to use for z greater than 0.1 or so. You will not need to compute with this
equation in this class.
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Practice Questions
1) Helium normally emits light at 5016.Å, but you receive this light at 5011Å , how fast are you
moving compared to the source?
2) You plan to go to the Moon. Your speed might be as large as 1 km/sec both coming and
going. If you transmit a signal to NASA at 2 m wavelength, what is the range of wavelengths
that will be received?
3) You observe a Nitrogen line at 4155.6Å . It is normally seen at 4152.0Å. What can you tell?
4) You are planning to send a probe to Mars. If the probe goes at speeds up to 25 km/sec in
either direction, and if it sends 0.5 m radio waves, what is the range of wavelengths you
receive?
Ans 1) -299.043 km/sec , be sure to use 5016Å in the denominator. Negative velocity means that
you and the source are getting closer together. You cannot tell what or who is moving. 2) Your
-6
speed would cause a Doppler shift (Δλ) of ±6.6667x10 m. This is NOT the wavelength that is
received, this is just the change in the wavelength. It can take either positive or negative sign
because the path to and from the Moon is both approaching and receding from the Earth. To get
the wavelength actually received, this change is added to the original wavelength. So the range of
wavelengths actually received is from 2.0000067 to 1.99999333 m. In this case, it is necessary to
keep enough digits to demonstrate the effect of the Doppler effect 3) You and the source are
getting further apart at 260.12 km/sec 4) From 0.50004167 m to 0.499958333m.
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Chapter 9 The Solar System-Overview
I. What is in the Solar System?
The Solar System consists of the Sun and objects that orbit the Sun; eight planets and their
moons, comets, asteroids, dwarf planets, small Solar System Bodies, gas and dust. We have
visited only the Earth and our Moon in person. We have sent landers to Venus, our Moon, Earth,
Mars, Titan and the asteroid Eros. We have sent spacecraft to orbit Mercury, Venus, Mars,
Jupiter, and Saturn and have flown by Uranus and Neptune as well as several comets and
asteroids. A probe entered Jupiter’s upper layers in 1995 and another landed on Titan (Saturn’s
moon) in 2005. The New Horizons mission will reach Pluto in 2015, Charon and proceed into the
Kuiper belt. And Mercury Messenger is orbiting Mercury and will begin mapping in 2011. Solar
system exploration has exploded since the 1960’s. So what can we say about our Solar System
and how does it compare with bodies orbiting other stars?
Even the definitions of the constituents of the Solar System are changing. Generally our Solar
System consists of one star, the Sun, the things that orbit it, and material that is flowing out of it,
the solar wind.
Until August 2006, there was no agreed upon definition of a planet. Then the International
Astronomical Union (IAU) voted to define a planet as a celestial body that (a) is in orbit around
the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it
assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighborhood
around its orbit of other objects orbiting the Sun. . Dwarf planets are also spherical and orbit the
Sun, but have not cleared their neighborhoods of other material. Even smaller objects that orbit
the Sun would be called “Small Solar System Bodies”. These definitions really apply to planets
in our Solar System, rather than objects orbiting other stars. The definitions were studied and
debated, but they don’t have the force of law and might be changed in the future.
In June 2008, the IAU also defined plutoids, as dwarf planets that are further from the Sun than
Neptune. Pluto is both a dwarf planet and a plutoid.
Speaking generally, planets are not only objects that orbit the Sun. We have discovered planets
orbiting other stars. And gravitational interactions among planets, dwarf planets etc can change
their orbits, often causing low mass objects to escape from the star. I don’t know what the name
would be then.
Planets are distinguished from stars, because planets are unable to cause nuclear fusion in their
interiors. That normally means that they have less than about 13 times as much mass as Jupiter,
if there are made of hydrogen and helium
Asteroids orbit the Sun, many in the area between Mars and Jupiter. But some come closer to the
Sun than the Earth and others go to further out than Saturn. Some asteroids seem to be rocky,
others are probably icy, and still others only very loosely consolidated, like rubble or dust bunnies.
Asteroid orbits are largely near the same plane as the planets’ orbits.
Kuiper Belt Objects are probably like Asteroids, but their orbits are largely outside of Neptune’s
orbit and they are more icy than rocky.
Comets are distinguished from asteroids because they form tails as they come close to the Sun.
When comets are far from the Sun, they are entirely frozen and cannot be distinguished from
asteroids. Comets are mixtures of dark, rocky material and ices. The ices are frozen when the
comet is far from the Sun. They are partly vaporized by sunlight as they come close to the Sun.
The solar wind, particles from the Sun rushing away at hundreds of kilometers per second,
pushes the vapor in the direction away from the Sun. The vapor reflects sunlight, resulting in the
comet-tail appearance. The comet never regains the material from the tail. So comets lose mass
each time they pass near the Sun. Eventually comets break up and disintegrate. Often particles
that break loose follow the same orbit as the comet. When the Earth passes through the stream
of particles, we experience a meteor shower.
Moons orbit planets. Some moons are just a few kilometers across. There are many moons
whose sizes we don’t know. All we see is that they reflect sunlight, but we don’t see their edges
Chapter 9
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1
clearly. They might be large and shiny, so only a single point reflects back to us. Or they might 122
be small and rough surfaced. The largest moon, Ganymede, is larger than the planet Mercury.
As of Dec 2007, 163 natural satellites have been discovered orbiting our planets. Surely there are
more.
As Kepler thought and the figures show, the planets’ orbits are ellipses, not circles. In OUR solar
system, the planets’ orbits are quite near circles (low eccentricity) and the planets all orbit going
the same direction. Venus, Uranus and Pluto spin retrograde. Some moons of the planets orbit
retrograde, as do some comets.
Pluto’s orbit is the more eccentric than those of the planets in our Solar System. That is, Pluto’s
orbit is the furthest from being a circle. But even Pluto’s orbit looks rather like an off-center circle
around the Sun. Comets’ orbits and orbits of planets orbiting stars other than the Sun have even
more eccentric orbits.
Pluto’s orbit carries it inside of Neptune’s orbit, but the
orbits never intersect. Since Pluto takes 1.5 times as
long to orbit the Sun as Neptune does, the two planets
never collide. (It is rather like model trains using some
of the same track. They are synchronized so there are
no collisions.) It isn’t chance. Gravitational interactions
with Neptune have nudged Pluto into this relationship.
Simulations of interactions between Pluto and the
planets indicate that changes (perturbations) in Pluto’s
orbit build up so that in perhaps 50 Million years,
Pluto’s orbit will change substantially.
The overall size of the Solar System is determined by
the size of the orbits of the outermost bodies. These
are comets (with no tails) orbit in a nearly spherical
region surrounding the planets’ orbits, called the Oört
Cloud (after Jan Oört). The Oört Cloud starts outside
Pluto’s orbit. We think it goes about about
150,000 AU, roughly half way to the next
nearest star. In 2004, an object called Sedna
was discovered. Its orbit takes it so far away
that it is probably part of the Oört cloud.
Current theories suggest that the comet
nuclei, small bodies of rock and ice, were
formed closer to the Sun than the Oört Cloud,
in regions where there was more material.
After the comet nuclei formed, gravitational
interactions with the early planets threw them
far from the Sun.
We would like to find the sizes, masses, and
composition of the planets. But, how is that
done?
II
Finding
Planets’
Distances
and
Diameters
Copernicus found the sizes of the planets’
orbits in terms of the Earth’s orbit. His
methods and results were basically correct.
Even when Kepler realized that the orbits are
ellipses, the overall sizes of planets’ orbits
were little changed.
Copernicus did not really know the distance
between the Earth and Sun. He knew about
Chapter 9
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2
Aristarchus’ estimate that the Sun is 1200 Earth radii away and he knew about Eratosthenes (and 123
also later astronomers’) estimates of the size of the Earth. But as we learned, Aristarchus was
wrong, the distance to the Sun is really about 24,000 earth radii from Earth.
The actual distances of the planets in kilometers were not known until Cassini measured the
parallax of Mars in 1672. He used a baseline from Paris to Cayenne (France). Mars was at
opposition at the time. That is when Mars, Earth and the Sun are all in a straight line with both
planets on the same side of the sun. He already knew that this distance was 0.523 AU. Parallax
gave him the equivalent of this distance in kilometers. Once the distance to Mars was known, the
distances to the other planets followed.
When the distance to a body is known AND the edges of the object are seen, so the angle it
takes up is also known, the linear size is easily computed.
All of the planets are large enough and close
enough that astronomers have now observed
the angle they subtend. The distances to
them are computed based on the positions of
the planets in their orbits. Once we know the
angle subtended and the distance, we can
solve the equation above for the diameter.
The radius and volume follow immediately.
This method is not generally used for stars. Stars are usually larger than the planets, but they are so far
away that most telescopes cannot tell their size. Telescopes are now being built which operate in groups of
two or more, called interferometers. They can distinguish the disks of some of the closer, larger stars.
III Finding the Mass
Finding the mass of any large body depends on observing its gravity and it assumes that gravity
is applicable. Combining the law of gravity
and Newton’s second law
acceleration due to gravity force is
. The
. Dividing by m1,
The acceleration of a body due to gravity from another depends only on the distance and the
mass of the other body. As we track the motion of a moon or a space probe, we can find the
mass of the body attracting it. This is why heavy and light things fall with the same acceleration.
Another way to measure the mass of a distant body is to use the formula for circular velocity
when we know Vcirc and r, the radius of the orbit, we can use the known value of the constant G
and solve for m2.
For things orbiting the planets in our solar system, we can normally measure r from the apparent
angular size (same method as measuring the planet’s diameter).
To find Vcirc, the Doppler effect can be used or we can watch to find the time to complete the orbit,
and use r, via
Distance = Rate x Time=Vcirc x Time for orbit = 2πr So, rearranging
Vcirc = 2πr /Time for orbit
This method of using the effect of gravity on an orbiting object to infer the total mass is the basis
for all of our knowledge of masses of galaxies, groups of galaxies quasars etc. Then the amount
of mass computed from Vcirc is compared to the mass inferred from counting the stars, planets,
gas, and dust. Surprisingly the mass of the observed bodies is nowhere near enough. When
Chapter 9
The Solar System
3
“dark matter” is discussed, this is the extra material needed to make the observed effect of 124
gravity above and beyond the amount of material attributable to the stars etc. More than 90% of
the “normal” material in the universe is thought to be dark matter. It is called dark matter, because
no light or particle radiation is observed coming from it. Only the effect of its gravity is noticeable.
In 1998, it was discovered that there is a repulsive effect operating in the Universe that is about
2.3 times as strong as the gravity of the dark matter. This is called “dark energy” and its effect is
mainly seen in the relative motions of clusters of galaxies, not within smaller objects.
IV Evidence of Internal Composition
The composition of the interior of large bodies cannot be sampled directly. We infer it by
modeling the interior. This same modeling procedure is used for stars and for planets.
The first indication of the interior construction of a body is the density. Density is defined as the
mass divided by the volume (Mass/Volume). We find the density from knowing the mass and the
3
radius of a body,R, and using the formula Volume =(4/3)πR to get the volume, then dividing.
How does the density help? Imagine holding a full quart size milk container. It holds a little more
3
than a liter of volume and a liter is 1000 cm (1kg/liter). Water and milk both have a density of 1
3
3
gram per cubic centimeter (written gm/cm ) or, equivalently 1000 kg/m . On the other hand, the
densities of some common materials are
Air at sea level.
Water
Rocks
Iron
Gold
0.0012 gm/cm
3
1 gm/cm
3
3-5 gm/cm
3
7.8 gm/cm
3
19.2 gm/cm
3
=1.2 kg/liter
=1 kg/liter
=3-5 kg/liter
=7.8 kg/liter
=19.2 kg/liter
3
=1200 kg/m
3
=1000 kg/m
3
=3000-5000 kg/m
3
=7800 kg/m
3
=19200 kg/m
3
So, when we find that the Earth has an average density, 5.5 gm/cm , can we know what it is
made of exactly? Could it be made of all water and air? All rock?
3
There is no way to average air only or rock only to make an average of 5.5 gm/cm . We know
from the surface that the Earth includes some water and rock, so we must also include some
3
material with density higher than 5.5gm/cm to get the correct average density. The interior of the
Earth is compressed by gravity due to the overlying layers. So material in the interior is denser
than the same material would be if it were at the surface.
To figure out the composition of the planets, we choose common materials that might give the
correct density and make a mathematical model of the planet. If the mass, radius, surface
temperature and other features of the planet predicted by the model match what we observe, we
accept the model as being valid, at least until we find out some new fact that contradicts them.
Which are the common elements anyway? When we look at our bodies or the Earth, we get a
Chapter 9
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4
very different picture of the situation than we get from stars and from gas between the stars. The 125
first chart shows numbers of atoms different elements in the Solar System overall. Since the Sun
includes about 98% of the material in the Solar System, it dominates the abundances. The
vertical scale is the number of atoms compared to the number of Hydrogen atoms. As a
12
reference, the number of hydrogen atoms is set at 10 . As you can see, the number of hydrogen
atoms is nearly 10 times the number of helium atoms. All other types of atom are far less
common. We find these abundances mostly by analyzing the Sun’s spectrum. (For some parts of
the curve the abundances from meteorites are used.) Abundances of elements in the Universe as
a whole are thought to be similar to those for the Sun.
This may seem odd. The Earth is NOT mostly hydrogen. We don’t have direct information about
the interior of the Earth, but the elements in the crust are very different. And the core is dense,
not
like
Hydrogen.
The
relative
abundances
of
elements
in
Earth’s crust are
shown in the
chart.
So why does the
Earth
have
different elements
from
the
average? Do all
the planets have
different elements from the average? Do all the planets have the same composition?
V Jovian and Terrestrial Planets and the Formation of the Solar System
The planets in our solar system generally fall into two categories, the terrestrial planets and the
Jovian planets. The terrestrial planets are similar to the Earth, as the word “terrestrial” indicates.
Jovian planets are similar to Jupiter. Jove is another word for Jupiter, the god. Mercury, Venus,
Earth and Mars are the terrestrial planets. Jupiter, Saturn, Uranus, and Neptune are the Jovian
planets. Little Pluto fits into neither category. It is probably much like other Kuiper Belt objects
(asteroid or comet like objects orbiting the Sun at distances 35-50 AU).
The terrestrial planets are closer to the Sun and can be even denser than rocks. So we expect
that they are not primarily of hydrogen and helium. The Jovian planets are found further out from
3
3
the Sun. They are far less dense, with densities from 0.7 gm/cm for Saturn to 1.64 gm/cm for
Neptune. This is much denser than hydrogen. The Jovian planets are larger in both mass and
radius than are the terrestrial planets. Differences in composition, mass and distance from the
Sun are likely related to the way that the Solar System formed.
Summarize the features of the different types of planets below.
Feature
Terrestrial Planets
Jovian Planets
Number of moons
Time to spin
Rings
Surface features
Internal energy sources
Density
Mass
Radius
VI Formation of the Solar System
We think that the Solar System was once a single cloud of gas, with roughly the same
composition as the Sun. That is, 90% of the atoms were (and are) hydrogen, and ~9% helium
with less than 1% everything else. As the cloud contracted, the densest part contracted to
become the early Sun, and heated up. This was a large part of the mass.
Chapter 9
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5
Gravity tries to pull together small masses of material as well. But as things are compressed, they 126
heat up. The gas pressure grows, fighting gravity. The Equation of State (ch 9 sec VIIi)
describes the relationship between temperature, density, volume and pressure. Different
materials can have different equations of state. (If you took chemistry, you may have learned the
Ideal Gas Law, PV=NRT or PV=ρkT. This is the equation of state for ideal gasses. Other
materials have other forms of the equation. For large masses, gravity wins over pressure and the
material contracts. For small masses, pressure resists gravity successfully, and the material gets
no more compressed. We think that for the Sun, gravity probably was sufficient to overcome the
pressure. A shock wave from an exploding star may have given the Sun’s material a push
As the gas cloud contracted, the part of the material that became the Sun got dense and hot. It
heated up the gas remaining around it. How then did the planets form?
Solid materials hold together because there are bonds between neighboring molecules or atoms.
We think that there was dust in the material that became the Solar System, because dust is seen
in distant gas clouds and even in the outer layers of stars. If dust particles happen to hit one
another, they may stick together building up to larger and larger bodies. We think that the dust
and other solid particles were able to hit and stick together forming larger bodies called
planetesimals. Eventually these planetesimals hit and stuck together into large enough bodies
that gaseous materials could be attracted and retained. The process of hitting and sticking is
called accretion. This is our best current idea of how the planets began to form.
What materials would make up the planetesimals?
There are some materials, called volatiles, are liquid or vapor at even low temperature compared
to room temperature on Earth, like hydrogen and ammonia. Other materials, called refractories,
are solid to high temperatures. Examples of refractories include iron and silicates.
The terrestrial planets are close to the Sun. It is and was warm there, only the refractories would
be available in solid form to hit and stick, and to start planet formation. But referring to the
abundance chart, we can see that there is very little of the materials that can make these
refractories. The terrestrial planets formed out of this comparatively unusual material.
Estimates of the temperature in the gas at the time the planets formed, indicate that starting at 4
AU from the Sun and going further, water (H20), ammonia (NH4) and methane (CH4) all become
solid, available to hit and stick. Referring back to the chart of the abundances of elements in the
Sun, it is apparent that Hydrogen is the most common element. Hydrogen alone does not solidify
except very low temperature (13.8K). The next most common element, Helium, forms no
compounds and doesn’t solidify until 0.95K. The Solar System was and is too hot for these
elements to solidify.
The next most common elements are Carbon, Nitrogen, and Oxygen. These are the very things
that combine with Hydrogen to make water, methane, and ammonia. So these materials are quite
common. Planets that can accrete these materials are able to grow large, because the cloud that
formed the solar system contained a large percentage of these materials.
The solid material, both refractories and volatiles, hit and stuck, accreting into cores for these
distant planets. If the mass of the core is large enough, it can attract the still gaseous (but
plentiful) hydrogen and helium, making the large Jovian planets. Jupiter and Saturn seem to have
formed at a distance where the Solar Nebula had a lot of mass and where water and ammonia
were solid. So they grew very large. At large distances from the Sun, the mass in the nebula
probably decreased and the mass of the planets formed decreases with it. Thus the planets get
smaller after Jupiter. The very distant Kuiper Belt and Oört Cloud objects were probably formed
closer to the Sun and later thrown there by the gravity of the massive Jovian planets.
As the early Sun matured, the solar wind began. The solar wind, particles of the Sun streaming
outward at hundreds of kilometers per second, pushed the remaining gas out of the Solar
System. This stopped the planets from growing any larger. There were still planetesimals
around. They were too dense for the solar wind to have much effect. Many of them crashed into
the larger planetary bodies during the first billion years of the Solar System.
Chapter 9
The Solar System
6
So it seems that there is an explanation for the Jovian and terrestrial planets in our Solar System. 127
In fact, it seems that Jovian planets would have to be formed far from the star and terrestrial
planets formed near the star. On the other hand, it isn’t this way in all systems with planets.
Birth of the Solar System
1 Once upon a time,
there was a cold cloud
2 Gravity pulled it to contract.
Possibly gas from a
supernova (star explosion) hit the cloud
compressing it and helping it contract.
3 As the cloud contracted, the gas collided.
Random velocities cancelled, while the common
velocity causes the cloud to spin.
4 The center of the cloud contracts
fastest, becoming the Sun.
A disk of gas and dust called the
Solar Nebula is left behind
5 Early Sun was MUCH larger and brighter than Today.
Solar Nebula near Sun was hot, further out colder.
6 Solid particles can hit and stick,
building up to larger bodies, called
planetisimals. Only a few materials are solid
near the Sun, more are solid far from the Sun.
7 The largest planetesimals can attract gas,
increasing the size of the final planet. The larger
planets change the orbits of smaller nearby ones.
8 Solar Wind, gas from the Sun,
pushes the remaining solar nebula gas,
quenching planet formation
VI Extrasolar Planets, planets orbiting stars other than the Sun.
In 1995 the first detections of planets orbiting other stars were made. Since that time, more
planets are discovered nearly every week. The most current count of planets found and the
methods used to find them can be found at http://exoplanet.eu/.Similar information and a cool
simulation can be found at http://planetquest.jpl.nasa.gov/atlas/atlas_index.cfm .
There are several methods that have, so far, succeeded in detecting planets. The easiest planets
to detect are very massive ones that are close to their planets, and these are the majority of the
ones that have been found so far. Unlike our solar system, we often find Jovian planets (gas
giants) close to the star. That seems an unlikely place for them to form, since the volatiles cannot
be solid there. Simulations of the possible evolution of the orbits of these planets indicate that the
planets could have formed far from the stars and their orbits been changed by the effects of other
planets (or possibly passing stars) so that they come closer to their stars later. These orbits may
well cause the planet to evaporate.
Chapter 9
The Solar System
7
128
How can we detect these planets?
Light Detection The most obvious way to find a planet is to see its light. In most cases, this is
harder than it sounds because the star that is orbits is far brighter than the planet so the planet is
lost in the glare. It is a trade off between being able to get the planet out of the glare of star light
and having enough light and enough motion to detect. It is not enough to just detect the light from
the planet, it is necessary to detect the motion of the planet to know that it is not a distant or very
faint star. Spectra of the planet can be used to tell whether it is a star, distant faint galaxy or a
planet. As of July 2009, 11 planets have been found by imaging them directly. The stars are
typically much less massive than the Sun.
B. Detection by Microlensing When an object comes between us and a source of light, gravity
from the foreground object warps space and light from the background object follows the
bending. The effect of the bending is that the background object appears brighter for a while
something is in front of it (not blocking it). If the foreground object is a star, there is one
brightening event. If the foreground object is a star plus a planet, the background star brightens
for a longer time or two separate times. . The duration of the brightening indicates the size of the
foreground object. As of July 2009, 11 planets have be detected that way.
C. Detection by Dynamical Effects Most of the planet detections so far are due to observations
of the motion of the star they orbit. This occurs because the force of gravity from each body acts
on the other. Since both star and planet experience a force, each experiences acceleration and
consequent motion. Depending on the direction to us compared to the orbit of the planet, the star
may move mainly toward and away from us or basically in a small circle as we see it.
Planet
x
star
Gravity of planet and star
cause them to orbit the center of mass
Motion of star is toward and away
from this observer, causing Doppler effect
xxx
x
x
xxx
x
The
toward-and-away motion has
been noticed, largely by measuring the
Doppler Shift of the star. This tells the
actual speed of the STAR as it orbits
the center of mass. Using the formula
for circular velocity, our knowledge of
the mass of stars, and Kepler’s laws,
we can estimate the mass of the
unseen companion. In many cases it
appears to be the right mass for a
planet.
This same effect, Doppler shift of the
light from the Sun, could be used by a
distant observer looking at the Solar
System. The distant observer would
see mostly the 11.8 year period of the
Sun in response to Jupiter. This is
because Jupiter is much more massive
than the other planets. In fact, it is
Motion of the star can be a
small circle as seen face on
more massive than all the other planets
put together. The other planets would
have an effect, so the Sun would move
in a complicated motion. An observer
would need to measure the motion of a
star until it had completed at least half a cycle to be sure that the motion was due to a planet.
Having nine planets makes the motion of the Sun more complicated. The small planets, like us,
have little effect and are likely to go unnoticed for quite a while.
Massive planets close to their stars are the ones that are easiest to find. They produce a strong
gravitational force and they change the direction of the force on the star quickly. So the observe
can find the pattern of the star’s motion quite quickly.
If the orbit of the planet is edge-on to the observer, the motion of the star shows up as a Doppler
shift. If the orbit of the planet is face on to the observer, the star’s motion shows up against the
Chapter 9
The Solar System
8
background of other stars. As of July 2009,1 plantet had been found that is face on, and 277 that 129
are detected by Doppler shift.
C. Detection by Changing Amount of Light-Transits and Eclipses
Once in a while, the planet lines up so that it comes directly in between us and the star, as it
orbits. The planet is smaller size than the star and colder. So when the planet is in front of the
star, the amount of light that we get is decreased. This is called a transit.
Halfway around the same orbit, the planet will go behind the star, and again the total amount of
light we get will again decrease. This is called an eclipse. When the planet is eclipsed, the total
amount of light decreases again, but by a smaller amount, since the planet is cooler than the star.
It is not very efficient to look for planets by waiting for transits, but in some cases, planets that we
know about from radial velocity curves have also had transits. The great thing about a transit is
that the radius of the planet can usually be found. The Doppler shift of the star and models of
stars tell us the mass of the planet, So when we combine the mass and the radius of the planet,
we can find the density and can tell whether the planet is a gas giant or a terrestrial planet.
Sometimes, when the planet is in front of the star, absorption lines from the planet’s atmosphere
can be seen (because the bright star shines through it). This indicates what the planet’s
atmosphere is made of.
As of July 2009, 59 planets have been found by detecting a transit.
D. Detection by Timing - Pulsar Planets
In a few cases the planets are found orbiting pulsars, dead stars that spin very fast and sweep
beams of optical and radio radiation past the Earth These beams are seen at very regular
intervals. The motion of the pulsar in response to the planet causes the time that we receive the
radiation to vary. Eleven planets have been detected this way.
VII Modeling the Interiors of Planets and Stars
To go from a measurement of average density to a model of the interior of a
body, astronomers use several simple concepts. For a spherical body, they
divide the body into layers and for each layer they have several equations to
solve.
1) Mass in Each Layer equals density times volume in the layer
2
(mass=4πr ρ)
2) Hydrostatic Equilibrium – force of gravity pushing in is balanced by pressure out
3) Equation of State –relates pressure, temperature, density, and volume. Different materials
and different states (like solid, liquid, gas) of the same material have different equations of state.
4) Heat transport – describes how energy from higher temperature interior layers is transmitted
out There are at least three ways that the energy can be transferred ,
Conduction-Particles collide with one another and transfer kinetic energy
Convection Regions of liquid or gas heat, expand, and may be displaced as denser, colder
material sinks in the presence of an overall gravitational field.
Radiation Photons carry energy between material. This is the only method that can work in a
vacuum.
The model will calculate the effect of all of these methods, though usually one dominates.
5) Energy generation- describes the amount of energy produced as a function of temperature,
pressure, density and composition. Typically planets generate a little energy from radioactive
elements. Stars generate energy by nuclear fusion.
The composition of the planet or star is guessed, based on the average density and any other
features observed. It need not be the same at every layer. Then a computer solves the equations
at each layer to find temperature, pressure, density etc. The total mass, the radius, and the
temperature at the outside of the body are compared with those observed. If not, the composition
is changed and the model computed again. The model must match all the observed properties.
Does this prove that the model is an accurate representation of the planets’ interior? No, of
course not. When additional information is obtained, such as a measurement Saturn’s flattening
from rotation, or detection of a magnetic field the model is revised. Planets’ models are being
Chapter 9
The Solar System
9
substantially revised due to the space program.
differences from one to the next.
Planets in our solar system exhibit many 130
When we use this same procedure on stars, it is a different matter. Modeling the interiors to
understand the way stars change over the course of their lives is one of the success stories of
astronomy. Stars start their lives as balls of gas, the same composition all the way through.
Nuclear reactions and gravity cause them to heat up and convert hydrogen into helium, governing
the stars’ temperatures and luminosities.
Computer models of stars at a variety of stages in their lives have been compared to some of the
many many stars we observe. The models have been modified to match the life stages of stars
quite well.
Questions:
1) What are three ways that you can tell a terrestrial planet from a Jovian planet
2) Define the solar nebula
3) The following are steps in the formation of the solar system. Put them in the order they occur
a) Planetesimals hit and stick b) Large planetesimals pull in gas with their gravity c)Cold gas
cloud contracts d ) Solar wind disperses gas e) Early Sun evaporates volatiles f) Sun heats up
4) Which of the following are part of the Solar System a) Milky Way galaxy B) Venus c) comets
d) Pluto e) Sirius f) Gas g) Virgo Cluster of Galaxies
5) What is the Oört Cloud? About how large is it?
6) What is the method we use to find the diameter of a planet in our Solar System (not Earth)?
7) How can we detect a planet orbiting a star other than the Sun?
8) Are the orbits of the planets in our solar system exactly circles? Which of the orbits is furthest
from being a circle?
9) What are volatiles?
10) What is accretion?
11) What can be told from the density of a planet?
12) What equations are used to model a planet or star? (the content, not the formula)
Planet
a, semimajor
axis of orbit
(average
distance
from Sun) in
6
10 km
a, semimajor
axis of orbit
(average
distance
from Sun)
in AU
P, period
of time to
orbit the
Sun in
Julian
Years
e,
eccentri
city of
orbit,
(no
units)
Orbital
inclinatio
n in
degrees
Mercury
57.909 0.387
0.241
0.206
7
Venus
108.209 0.723
0.615
0.006
3.394
Earth
149.597 1
1.000
0.017
0
Mars
227.937 1.524
1.881
0.093
1.85
Jupiter
778.412 5.204
11.856
0.048
1.305
Saturn
1426.725 9.537
29.423
0.054
2.484
Uranus
2870.097 19.191
83.747
0.047
0.77
Neptune
4498.253 30.069
163.723 0.008
1.769
Pluto
5906.376 39.482
248.021 0.248 17.142
Data from Allen’s Astrophysical Quantities, Fourth Edition, 2000.
Chapter 9
The Solar System
Mass
24
in 10 kg
.33
4.869
5.974
0.642
1898.7
568.51
86.849
102.44
0.013
Equatorial
Radius
in km
2239.7
6051.8
6378.14
3397
71492
60268
25559
24764
1195
Rotation
Period in
solar
(Earth)
Days
Inclinati
on of
Rotatio
n Axis
in
degrees
58.646
-243.01
.997
1.026
0.413
0.444
-0.718
0.671
-6.388
0.0
177.3
23.45
25.19
3.12
26.73
97.86
29.58
119.6
10
131
10 The Earth, Our Point of Comparison
As of July 2009, humans have visited only the Earth and our Moon. Unmanned machines from
Earth have landed on Mars, Venus, Titan, the asteroid Eros and our Moon. And we a probe has
entered Jupiter’s atmosphere. Since our experience with other planets and moons is so limited,
we tend to use the Earth as a point of comparison and then compare and contrast the landforms,
mountains, rivers, glaciers and oceans floors on the Earth can be compared with the features on
other planets and their moons.
On the Earth, we see the effects of wind, water, the molten interior, and life. Wind and water are
felt by each of us and also produce erosion. Effects of the molten interior can be seen in
movements of the continents, mountain building, positions of volcanoes, and the presence of the
Earth’s magnetic field. The overall theory of how the surface responds to the Earth’s heated
interior is called plate tectonics. Life on Earth has altered the carbon dioxide in our atmosphere,
produced limestone and caused much of the break up of rocks into soil.
Plate tectonics can be summarized as follows. The surface of the Earth appears to be divided
into major sections, called “plates”. The plates are moved around on a slippery layer, called the
asthenosphere due to convection currents in the next layer down, the mantle. As we go into the
interior of the Earth, models, experience, and earthquake evidence lead us to think that the
temperature increases with depth. The outer core is interior includes liquid, while the even hotter
inner core is solid.
Plates under the oceans can be less than kilometers thick. Under land, they can be as thick as 50
kilometers. But the granite that makes up land is less dense than the basaltic ocean floor. Plates
move away from one another where magma is oozing up from the interior of the Earth. Since
there is no extra space on the surface of the Earth, they collide and the thinner oceanic plate
slides under the land. This wrinkles the land, causing folded mountains, Earth’s most common
kind. The plate boundaries are shown below. Small circles are locations of active volcanoes.
Earthquakes occur more often under the boundaries of the plates. Volcanoes occur most often
above places where sea plates are sliding under land.
Modified from
Tilling, Heliker and Wrigley,
1987 and Hamilton1976
Sometimes the plates move past one another, rather than colliding head on. This is what is
happening with the famous San Andreas Fault and also with the Hayward Fault. The San
Andreas Fault runs along the San Francisco peninsula, west of route 280 and under the San
Andreas Lake and the two Crystal Springs Reservoirs. It goes out to sea at Daly City and comes
back in at Bolinas. In the other direction it extends to near Los Angeles.
Today we can measure the actual change in position from one continent to the next, by direct
measurement. The speeds typically average several centimeters per year, but some plates and
parts of plates move freely and others are stuck. Typically earthquakes occur near plate
boundaries. Earthquakes are especially strong, when the locked parts let loose. During the 1906
San Francisco earthquake, the fault moved about 8 feet on the peninsula. But some of the
southern parts of the fault have been locked together, and not moving throughout that time. That
is why people are predicting an earthquake near Parkfield, one of the stuck places.
Chapter 10
Earth, Our Point of Reference
1
132
Alfred Wegener (d 1915) suggested that Africa and South America were once joined. The lump of
Brazil would have fit into the notch below Equatorial Africa. The land animals and plants are not
the same today on these two continents, but there are fossils, from more than 60 million years
ago that are the same.
Wegener was not believed during his lifetime. But the evidence accumulated and by the late
1960’s scientists became convinced that the continents were, indeed, moving. How did this come
to be? It is a long story.
Over the years, people measured the effects of earthquakes. These effects (besides fear,
destruction etc.) appear in the form of earth motion. Seismographs at a variety of distant locations
record the motion in each direction. As people observe the vibrations from earthquakes, they use
mathematical models to see how the vibration has traveled through the earth and where it came
from. Whenever we have an earthquake, you will hear the announcement of the “epicenter”. This
is the location on the Earth’s surface directly ABOVE the source of the earthquake waves.
As people traced back earthquake effects, they follow several types of wave. There are surface
waves (along the surface only), P waves and S waves. The P waves are also called primary or
pressure waves. They are primary because they travel faster through the Earth and arrive first.
The second waves to arrive, S waves or secondary or shear waves have a different pattern as
shown.
Undisturbed
Layers
Surprisingly, it was found that P and S waves could
not be seen from everywhere on Earth. It was not
that the instruments were insensitive. It was found
that both P and S waves could be seen near the earthquake epicenter. Then neither could be
detected. And then on the side of the Earth opposite the earthquake, the P waves were detected,
but not the S waves.
P wave, material is
along the direction of wave
compressed
motion
T
i
m
e
Because of the way that the S wave moves
material side-to-side, S waves will not travel
through a fluid (liquid or gas). The P wave,
however, will go through solid, liquid or gas.
(Sound is a P wave and you can easily hear
speech as it carries through gaseous air, or
though solid walls. Sound travels through water
S wave, material
perpendicular
to direction
moves
wave
of
motion
as well, but it is pretty hard to talk under water.)
T
i
m
e
As people modeled the interior of the Earth and
tried to match the way that earthquake waves
travel, it was found that S waves cannot
complete paths that go within about the inner 2/3
of the Earth’s radius. This is consistent with the
presence of a fluid layer starting about 1/3 of the
way in.
Chapter 10
Earth, Our Point of Reference
2
133
As scientists modeled the overall structure of the Earth, using the equations in described in
chapter 9, they found that radioactive elements decaying and pressure from Earth’s gravity do
make it hotter inside than outside. The interior temperature is easily hot enough to melt rocks.
As time goes by, the amount of the radioactive elements decreases and so does the head they
provide. If we wait long enough (and the Sun does not vaporize the Earth first), the interior of the
Earth would cool off to the point where it would all be solid. That is probably the situation today
with small bodies like our Moon, Mars and various asteroids.
Our models of the Earth, supported by earthquake wave transmission data, lead us to an Earth of
the Earth pictured below. The Earth includes a solid inner core, a liquid outer core, a fairly
rigid mantle, and a thin solid crust. The slippery asthenosphere is between the Mantle and the
crust. The inner core is thought to be solid based partly on the high pressure and partly on the
observation that waves travel faster going north-south, than going at different speeds depending
on what direction they go. This is consistent with a partly crystal inner core, possible with a solid,
but not with a liquid.
The overall idea of a molten interior, at least
starting at the bottom of the mantle, dates from
the 1930’s. Evidence for the inner core with
crystalline structure has been solidified in the
1990’s.
Earth
Model
Mantl
e
Liquid Outer Core
By the early 1960’s special submarines were
able to observe the ocean bottoms. They found
Soli
that lava oozes up near the Mid-Atlantic Ridge
d
Inne
rCor
and the East Pacific Rise. The lava heats the
e
seawater
above
the
normal
boiling
temperature. The water cannot become steam
Crus
because it is under too much pressure.
t
Specially-adapted forms of life found near
these hot spots survive from the energy of
chemical reactions in the material coming from
the interior. Finding these life forms has
Convectio
n
substantially expanded our concept of where
and how life can exist. Actually observing places where magma is coming up was a powerful
demonstration that the plates might have a reason to move. So scientists looked at points at
varying distances from the mid-oceanic ridges, they were able to observe
a) The seafloor got older and older going away from the ridge
b) The seafloor is magnetized in changing directions.
How could anyone decide on the age of a rock?
Finding the ages
As geologists (and you) look at layers in rock or dirt or dirty laundry, there is an initial presumption
of age. Where would you say is the oldest part of the heap in the figure?
Given that the layers of stuff appear horizontal, we would expect
that the lowest level is the oldest. We don’t know for sure HOW
Up
old unless there is something with a definite date, like a
Younge
newspaper buried or unless we have an accurate idea of how
r
fast material is accumulating. Early geologists estimated the
rate that rocks and earth would accumulate and estimated the age of the Earth to be at least a
9
th
Billion (10 ) years. They did not have any way to get an age in years until well into the 20
century.
What would happen if there were several sets of layers, like in this figure? You could reasonably
expect that the top layers are the youngest, but there is no way to tell whether the layers in the
right hand pile are older or younger than the others, because there is no overlapping relationship.
As here, the layers are not generally identical at widely distant points.
Chapter 10
Earth, Our Point of Reference
3
134
To get a relationship between these distant layers, we might use fossils found in each area.
When a fossil is found in a layer, at least we can be sure that the layer was formed during the
time that the particular type of creature was alive. This pins down the age of the layer somewhat.
Typical species are around for ~ 5-10 Million years (not the individual plants or animals, the
species), but some species change little over much longer times. And some fossils are not
readily identified with fossils in other locations.
To get an actual age for a rock layer, the best way is to use radioactive dating. This is how we
can find absolute ages for the seafloor. To use radioactive dating, it is important to understand
how it works.
Main
Remaining
We often think of atoms and their
Part
nuclei as permanent, going on
becomes
forever. But many nuclei are
unstable.
They
fall
apart
spontaneously, without our doing
anything. The falling apart process is
called “radioactive decay” even
though it has nothing to do with rot or
fungus.
When a nucleus falls apart, it doesn’t
just disappear. Usually it becomes
one comparatively large nucleus,
called the daughter, and a variety of
smaller pieces (It’s like when you
pick off a piece of a muffin. Most is
left, and then there are crumbs).
Some of the pieces are shown in the
figure. Often when people talk of
“radiation” they mean the results of a radioactive decay. In general it is not beneficial to get hit by
these smaller pieces.
The timing of radioactive decay is what makes it useful for measuring dates. Each nucleus
generally falls apart in the same way. They don’t get old, wear out, and fall apart (like us). They
have a fixed probability of falling apart every second. The probability depends on the type of
nucleus, but nothing else. People measure the probability of decay in the laboratory and then
apply the knowledge to samples of rocks, bodies etc.
A plot of the decay of a hypothetical nucleus is shown below. The plot has two curves. One is the
amount of parent, the original nucleus. The other is the amount of daughter, the nucleus that
results
from
decay.
The
vertical
axis
shows
the
amount of each
type of nucleus.
It is given in
relative terms.
That is 1, or
100%, is the
starting position
for the parent. It
doesn’t
mean
that something
needs to be
made of 100%
parent; it means
that
whatever
Chapter 10
Earth, Our Point of Reference
4
135
amount of parent you started with is all there.
Often people characterize the way a nucleus decays by its half-life. The half-life is the time for
half of the existing parent to decay into daughter. After waiting one half-life, there is 50% as much
parent as we started with. After two half lives, there is 25%. After 3 half lives, there is 12.5%.
Theoretically, the amount of parent is halved each time one half life goes by.
As can be seen, the amount of daughter increases as the amount of parent decreases. This is
because every time a parent nucleus decays, it becomes a daughter nucleus and some “crumbs”.
At every time, there is a unique combination of amount of parent and amount of daughter. So if
we have a body and can measure the amounts of parent and daughter, we can find the age of
the body.
+5
It is written in scientific notation by a computer. The value 8.0E+05 means 8.0 times x10 . The
computer uses “E+05” to say, “The exponent of the power of 10 is positive 5.” It cannot write
superscripts, so it uses the “E”. People normally write 10 and an exponent, NOT E.
6
Considering this particular plot, each large division on the horizontal scale is 2.0E+05 or 0.2x10 .
The next number after 8.0E+05 is not 10.0E+05 because it must be in scientific notation (only one
digit before the decimal). So instead, it must be 1.0E+06.
5
4
The small divisions are 1/5 as large as 2.0x10 or 4.0x10 years, just the result of dividing the
5
number 2x10 (=200,000) by 5. Other types of nucleus will have different decay rates and
different horizontal scales, but the principle will be the same.
5
How old is the material above when there is 70% daughter and 30% parent? 7.0x10 years
When there is 30% daughter and 70% parent?
It may seem odd to bother with the daughter. If we were running a simple experiment, we would
know the amount of parent we started with and it would be unnecessary to assess the amount of
daughter. In the real world, especially with rocks, we rarely know how much parent was present
to start. So when we measure the amount of parent in a rock, we don’t know what fraction of the
original is left.
IF both the remaining parent and daughter are still in the rock, one can add up
the amounts and find the original amount of parent. THEN it is possible to find the age. If the
daughter has been washed away or if it is a gas that has escaped, then the original total amount
is not known, and there is no accurate way to find the age.
(Minerals are rather like lemonade. You make lemonade with water, sugar and lemon juice. There is no
exact fixed amount of these different components, although there are limits to how much sugar you can get
to dissolve. Because you wouldn’t know the amount of lemon juice that you started with, it wouldn’t be
possible to know what fraction of it was left at some later time.)
Not every rock has any radioactive elements in it, and not every radioactive element allows us to
find the age of a rock. The amounts of parent and daughter give a good age determination when
there are substantial amounts of both present. When a sample has 99.99% daughter, for
example, it is hard to tell the age accurately. The amount of parent is so tiny it is hard to measure
and the amount of daughter is not sensitive to the age.
The properties of some radioactive elements are shown in the table. The number before the
element name tells the atomic weight, the number of protons plus the number of neutrons in the
nucleus. As you can see, in some cases the decay causes a substantial change in the atomic
number. In others, one neutron changes to a proton and the atomic number stays the same.
Parent
238
Uranium
235
Uranium
129
Iodine
40
Potassium
14
Carbon
Chapter 10
Daughter
206
Lead
207
Lead
129
Xenon
40
Argon
14
Nitrogen
Half-Life (years)
4.508x109
0.713x109
1.7x107
1.3 x109
5870
For rocks, elements like Uranium
and Potassium are useful. The
half-lives for these elements are so
long that there will surely be some
of the parent left in a rock. The
Argon produced when Potassium
decays is a noble gas. It does not
form compounds. So argon will be
Earth, Our Point of Reference
5
bubble out of a rock if it melts after the argon is formed. The age from potassium-argon dating 136
tells the time since the rock solidified.
14
You may have heard about Carbon 14 ( C ) dating. It is important, but never used for rocks. It is
only useful for things that were once alive and that have died within the last 30,000 years or so.
This is because the short half-life of
14
C means that it will be all decayed by
the time a rock has formed.
Carbon 14 is continuously created in
our atmosphere by the effect of cosmic
rays on the nitrogen. As we all eat and
14
breath, some of the C is incorporated
in our bodies. It is always decaying,
14
but we renew the C by eating and
breathing more.
When we die, the carbon changes to
nitrogen. Anthropologists often dig up
sites where people used to live. They
find bones and baskets (made of
reeds) and are able to find the time
since these things were alive from the
14
C dating. Carbon 14 dating has been compared with tree ring ages for the last several thousand
years, thus verifying its time scale. Trees form rings every year and the size of the ring depends
14
on growing conditions. So the rings and C both tell an age, and the ages can be corrected to be
the same.
How old is a sample with 90%
14
C and 10%
14
N ? (as shown in the plot)
So to summarize, we find ages by
a) Stratigraphic Dating , the younger thing is on top, if the layers are horizontal
b) Fossils tell that a layer was first formed when the species was living
c) Radioactive dating tells the actual age since the rock was formed
Back to Plate Tectonics
So as scientists looked at the rocks in the sea floor on either side of the mid –oceanic ridge, they
found that the further away from the ridge, the older the rocks.
They also found that the rocks at the bottom of the ocean are igneous rocks, that is rocks which
formed from solidification of lava or magma.
When these rocks solidified, they were magnetized by the Earth’s magnetic field. A magnetic field
is due to the orbits of the electrons in the
atoms aligning to one another, so that the
electrons have a predominant direction of
motion. The electrons can align when the
atoms move around as a melted material
cools and solidifies. Once it is solid, the
atoms do not move around very much and
the magnetic field remains fixed. If the
material is heated too much, even if it is not
melted again, the electron orbits realign. The
magnetic field can be lost.
When scientists examined the material in the
seafloor, they found that there were regions of reversing magnetic field, symmetrically placed on
the sides of the mid oceanic ridge. This is just what we expect for a seafloor formed in the
presence of the Earth’s magnetic field. For many years, geologists have noticed that as they dig
down into rock layers, the rocks have reversing magnetic fields. At least 92 magnetic field
Chapter 10
Earth, Our Point of Reference
6
reversals have been detected in just the last 118 million years. But there may have been more. If 137
the magnetic field reversed for just a short time, there would be few rocks magnetized by the
reversed field and it would be hard to detect.
The plot shows the history of the direction of Earth’s magnetic field over the last 10 million years.
The magnetic field has been in the same direction for about 780,000 years, an unusually long
time.
The Earth’s magnetic field has a consistent shape over the entire surface of the Earth, called a
dipole, as shown in the diagram. It is a little like the surface of an apple, with the North and South
magnetic poles at the stem
and flower ends of the
apple. Magnets, like the
magnet in a compass or like
the magnetic field of a rock,
line up just opposite the
magnetic
field
lines.
Because of this consistent
shape, we can relate the
direction of the field at any
two positions near the Earth.
You may notice that the
directions of the North and
South MAGNETIC Poles are
not the same as the North
and South GEOGRAPHIC
poles. Maps, latitude and
longitude are all referred to
the geographic poles. Many maps show the correction to
apply to the magnetic north direction (what a compass
shows). The magnetic poles wander around on a scale
of years, as can be seen in the figure.
Magnetic Field
to
North Celestial Pole
Rotation Axis
Magnetic Field Lines
compass needle lines
But why a magnetic field? And why does it change? We
up along these
think
that
the
rotati
on of
the
liqui
d
oute
r
core,
an
to
elect
South Celestial Pole
ricall
y conducting material, will generate electric
currents. These currents, in turn, result in
magnetic fields. As time goes by the
direction of the flow changes. Since
approximately 1995, computer simulations
that model the motion of the interior of the
Earth have resulted in magnetic field
reversals.
Regardless of exactly how the magnetic field
Chapter 10
Earth, Our Point of Reference
7
reversal occurs, the combination of the overall dipole shape and the worldwide reversals gave 138
scientists the clue they needed to map positions of the continents well into the past.
Remember, near the mid oceanic ridge the seafloor is magnetized in stripes. If we go back in
time, to times BEFORE these stripes of seafloor were present, the Atlantic Ocean was smaller.
Wegener was right, North America and Europe used to be connected, as did South America and
Africa. The compression of North America into Europe caused the wrinkles that are now the
Appalachian Mountains in the United States.
As we go further back in time, the stripes are not strictly parallel. Using the radioactive dates for
these stripes and forcing the magnetic field to a dipole shape, it becomes clear that the continents
were not all aligned as they are now, and their locations were very different. Current models go
back to about 650 Million years ago. At that time, the placement and size of the continents was
entirely different from today. Past positions of the continents will be discussed in class and can
be found from the Internet.
Is 650 Million years the entire age of the Earth, or of the rocks? Hardly. Based on models of the
Sun and on the oldest rocks from Earth and Moon, we think that the entire Solar System is about
4.56 Billion years old. So why don’t the models go all the way back?
For one thing, the seafloors are formed, then thrust under the continents and melted. Once the
crust has been melted again, there are no magnetic stripes and no radioactive dates. So it is hard
to establish just where the land and the ocean were. Also there are few fossils before about 550
Million years ago. There was plenty of life before that, but it had no hard body parts (skeletons,
shells etc). So again it is hard to trace.
What was the very Early Earth like then?
The very earliest Earth would have been melted due to heat from collisions of dust and later
planetisimals. The melted material would allow the denser materials, like Iron, to fall to the center.
This is consistent with both our models of the Earth and with the effect of its gravity on satellites
and the Moon.
The earliest atmosphere was hydrogen and helium gas from the solar nebula.
For the first 1 Billion years or so, there were many planetisimals left in the solar nebula. Many of
them collided with the planets (including the Earth), helping to keep them hot. A crust did form
over the molten interior, and the composition of the atmosphere began to change. Hot lava oozed
up from volcanoes. But as this happened, the atmosphere began to change.
When lava comes up from below the Earth’s surface, water (H2O) and carbon dioxide (CO2) are
released. Typically these molecules are dissolved in the lava when it is under pressure inside the
earth. As the lava reaches the surface, water and carbon dioxide come out of solution. They form
bubbles in the lava, and are released into the atmosphere. They formed a second atmosphere for
the Earth. The water, of course, was not only present as a gas. It formed oceans, lakes, and
rivers as well. The carbon dioxide formed the bulk of Earth’s atmosphere.
We can tell that the atmosphere was largely carbon dioxide from our observations
a) Anaerobic bacteria and other life forms are found now and in the fossil record.
Anaerobic means without air, in the sense of without oxygen. Some anaerobic life
forms cannot live in the presence of oxygen; others just do not use oxygen. These
were the dominant form of life before Oxygen became abundant in our atmosphere.
b) Minerals, like the Banded Iron Formation, that were formed in the presence of a very
low level of oxygen. Banded Iron Formation deposits with ages from 1.8 to 3.2 Billion
years demonstrate that there was less than 1% as much free oxygen when they
formed as is available today.
c) Molecules of Oxygen gas (O2 or O3).are not stable. They react readily with many
materials. To maintain oxygen in the atmosphere, it must be renewed constantly.
Today, and in the past, life forms release free oxygen. One easy indication that a
planet has life is oxygen in its atmosphere.
Chapter 10
Earth, Our Point of Reference
8
139
Even though there are few fossils before about 550 Million years ago, there are evidences of life.
One of the most striking is stromatolites. These are mineralized remains of colonies of singlecelled life forms. For a long time, stromatolites were not clearly identified as fossils. They were
thought to be just rocks. Then living stromatolite communities were discovered in some low
oxygen water off of Western Australia. The community includes bacteria that produce oxygen on
the outside in contact with the water, bacteria that cannot tolerate oxygen further in. As time goes
on, the outside layers die and their remains become mineralized. New layers of bacteria grow on
top, until the entire colony gets quite large. Entire decorative columns in China are built of the
mineral remains. The earliest known stromatolite colonies are dated to about 3.85 Billion years
before the present.
So how did there come to be free oxygen in our atmosphere? Green plants do, today, free
oxygen. But green plants and land-based life (as opposed to life in the oceans) developed when
oxygen levels were nearly as high as today. Oxygen levels rose from negligible levels to current
levels between abut 1.9 Billion years ago and 400 Million years ago.
We think that this was due to a combination of Carbon Dioxide dissolving in the oceans and some
of the carbon precipitating to the bottom and to the development of skeletons. Skeletons, in the
form of sea shells, use carbon. When the animals die, the shells are not all immediately recycled.
Many of them fall to the bottom of the sea. Some are compressed into the limestone we see
today, some of the seafloor is dragged back under the continents as a result of plate tectonic
motions. These processes reduce the amount of carbon dioxide in the atmosphere implying that
our atmosphere was once much denser. This is consistent with what we see on Venus. Venus’
atmosphere is mainly carbon dioxide and it is some 90 times as dense as is Earth’s. We think
that Venus has never had life or water to remove the carbon dioxide.
What is a better atmosphere? Oxygen or carbon dioxide? We humans cannot breathe carbon
dioxide. But plants do use it and it may be possible to breed plants to live in an all carbon dioxide
atmosphere. Many anaerobic bacteria cannot live in the presence of an oxygen atmosphere. So
for them, carbon dioxide is MUCH better.
Oxygen benefits life on land because it forms the molecule ozone (O3) as well as O2. Ozone is
toxic to us and is considered air pollution when it is at ground level. (You many have smelled it
when there is an electrical fire or lightning.) But ozone high in the stratosphere protects us from
some of the Sun’s ultraviolet light. Ultraviolet photons carry a lot of energy and can break up
molecules. When they hit our body, they can cause tanning, cataracts, and sometimes skin
cancer. When an ultraviolet photon hits an ozone molecule, the molecule can be broken up. The
energy of the photon goes into breaking up the ozone and into giving kinetic energy to the
resulting O and O2. This protects us in the same way that a bulletproof vest protects a person. If
a bullet hits a person in a bulletproof vest, the energy of the impact is spread out and the bullet
doesn’t go straight into the person’s flesh. When an ultraviolet photon is absorbed by the ozone,
the energy is spread out. It heats the atmosphere, but doesn’t get to break up our molecules.
Ozone in the stratosphere is not constant. During the winter, the ozone near each pole
decreases. Weather patterns isolate the air near each pole from the rest of the atmosphere
during the winter. In the spring, ozone-rich atmosphere from nearer the equator mixes with the
polar air and enriches the ozone. We have been monitoring the amount of ozone and finding
that the area with low ozone has been increasing and the amount of ozone in a column of air
above the polar region has been decreasing (at least up to about 2000). In the last few years the
amount of ozone has varied, but the hole has not really gotten larger.
Chapter 10
Earth, Our Point of Reference
9
This change may be part of some long-term cycle, but we think it is also part of a reaction to man- 140
made pollution. In the 1960’s and early 1970’s chlorofluorocarbons (CFC’s) were used as
propellant in spray cans and as refrigerant (the working fluid to make air conditioners and
refrigerators work). The CFC’s
were
released
into
the
atmosphere when the cans were
sprayed or when air conditioners
leaked. The molecules slowly
rose to the stratosphere where
we think that the chlorine atoms
become detached from the rest.
Chlorine is very reactive. It is
able to break up an ozone
molecule, rather than allowing
the ultraviolet light to do it. One
chlorine atom doesn’t just break
up one ozone molecule. The
chlorine atoms interact with the
atmosphere, are freed up, and
can break ozone after ozone so
long as the chlorine remains in
the stratosphere, expected to be
around 50 years.
When it was realized that the CFC’s would affect the ozone, a series of international treaties were
implemented. The goal was to limit the CFC release. At the time, there was no known substitute
for Freon, a refrigerant. In the last 30 years, substitutes have been found and refrigerators have
been redesigned. Based on these treaties and the smaller amounts of CFC’s released, we still
think it will take until about 2100 for the ozone level to come back to the level before CFC’s. The
worst time for the ozone is predicted to be around 2000-2001.
So ozone protects life on land from ultraviolet light. Life in the ocean is protected by the overlying
water. Oxygen dissolved in the upper levels of the oceans is what fish use for their respiration.
The deeper levels of the ocean have little oxygen, and (we think) much lower prevalence of life.
Carbon dioxide and water vapor have their own effects as an atmosphere. They are
“greenhouse gases”. They act to keep a planet warm.
To understand how the greenhouse effect works on a planet, go back to the idea of black body
curves. Dense bodies, like the Earth, give off energy like a black body. Depending on the
temperature, a black body gives off a specific amount of energy with a specific distribution of
wavelengths, as shown. The hotter the body, the more energy given off.
Most of Earth’s energy is from the Sun, which also gives off a black body spectrum (with overlying
absorption lines) consistent with its surface temperature, about 5800K. Some of this energy is
absorbed, some reflected. As the Earth absorbs energy, it heats up. It gives off energy according
to its temperature. Earth either heats or cools until the amount of energy it gives off just equals
the amount it absorbs. So?
The Sun produces a black body curve with a maximum near 5000 Å, visible light. On the other
hand, the Earth produces a black body curve with a maximum near 96,600 Å infrared light.
Carbon dioxide and water vapor both absorb light strongly in the infrared. These molecules
reemit the energy from the absorbed photons, but not necessarily in the same direction. So the
infrared radiation is prevented from leaving the planet. What happens? The planet has not given
off the exact same amount of energy that it absorbed. So it must heat up. As it heats up, the black
body curve changes to one that gives off more total energy. The planet heats up until the net
energy lost, even in the presence of the greenhouse gasses, equals the energy gained. This
changing temperature may change the cloud cover and/or the amount of snow. So the energy
gained might change too.
Chapter 10
Earth, Our Point of Reference
10
141
(Practical Note: The goal of glass
greenhouses for plants is to keep the
plants warm. The glass keeps infrared
radiation in, and also keeps cold breezes
from chilling the plants. Breezes matter a
lot for plants, but not for planets. Motion
of atmosphere of a planet just evens out
the temperature between the day and
night. It cannot change the average
temperature.)
SUNLIGH
5800 K
T
Blackbody
Reflected
Doesn't
light
Plane
Heat
t
PLANET
As you may imagine, it is not easy to
figure out how much difference the
Radiation from Planet to Balance
Some Infrared Radiation is
Energy
greenhouse effect makes. Estimates
by CO 2 or 2 O and sent
absorbed
H
back
for the Earth are that it is 35K (x 9/5
o
o
F/K =63 F) warmer today with the
current amount of carbon dioxide than it would have been without. Today only 0.038% of the
atmosphere is CO2. In the distant past, when there was a larger amount of carbon dioxide, the
greenhouse effect would have been larger. But also the Sun used to give less light.
o
Is the greenhouse effect a good thing? What would happen if the Earth were 63 F colder?
What would happen if the Earth were warmer? Has the climate really changed?
Over the years, the climate certainly has changed. At one level, we are coming out of an ice age.
Canada, Minnesota, Wisconsin, and Michigan were covered by ice. On a shorter time scale, we
know that Greenland had agriculture when the Vikings moved there in perhaps 800CE. By
1000CE, the climate had changed enough that they were looking for somewhere else to go (like
Vinland in Canada). It had become (and remains) too cold on southern Greenland. Some
scientists think that the Earth has had periods when ice covered the ocean surface entirely.
Based on estimates covering the last 550 million years or so, the current epoch is on the cool
side of a variation that covers about ± 10 degrees Fahrenheit.
On the other hand, can people cause climate change? Most scientists are in agreement that the
weather has been getting hotter since about 1850. Glaciers are melting and the Arctic (northern)
ice pack is getting smaller. Some estimates predict no Arctic ice by about 2020.
This global warming may be due to increasing levels of carbon dioxide in the atmosphere. Most
industrial processes burn fossil fuel and release carbon dioxide. Over the past 150 years or so,
since the industrial revolution, the carbon dioxide level in the atmosphere has increased by about
17%.There is great concern that if the ice caps melt and the oceans warm up, sea level will rise.
Florida would be largely under water. If the greenhouse effect increased enough, all the water
might vaporize. Without liquid water, the climate on earth would become very extreme, hotter in
summer and colder in winter. This sounds far fetched, but our twin planet Venus, is estimated to
be 400K hotter because of its extreme greenhouse effect.
Can we do anything to limit the greenhouse effect? There are international treaties being
negotiated to limit the amount of carbon to be released into the atmosphere in the future. A goal
of the 2009 international conference is to limit the carbon released with a goal of limiting the total
o
o
increase of temperature to 2 C (3.6 F) compared to the pre-industrial temperature level. This
would require that we decrease the amount of carbon we emit substantially. There is resistance
to limiting emissions because people think that it will cost too much money and/or limit economic
development. A current proposal is to have a cap and trade system in the US for carbon
emission.
Earth’s climate has varied substantially. A chart of the temperature history (and the history of
continental positions)can be found at http://www.scotese.com/climate.htm. According to this
o
history, Earth is near its coolest extreme and has been up to 13 C warmer in the past. The
causes of these major variations in temperature are not entirely known. The positions of
continents, the relationship between the Earth’s axis tilt and the closest point on the orbit, and the
evolution of life on Earth are all likely contributors. In the past, the Sun gave less energy. In the
far future, the Sun will be giving much more energy and we will surely be hotter/
Chapter 10
Earth, Our Point of Reference
11
Earth History
TIME (yr ago)
~14 Billion
Before the solar
system
4.5-4.6 Billion
3.8 Billion
2.5 Billion
3.2- 1.9 Billion
650 Million
550 Millions
400 Million
240 Million
225 Million
142
Event
Big Bang
Stars create atoms heavier
than Hydrogen and Helium,
Gas cloud which becomes
Sun and Planets exists,
Supernova explodes making
Aluminum 26
Formation of solar system
from gas cloud
Early Life
(really firm evidence 3.5 BY)
Earliest Known Glaciers
Oscillations in atmospheric
Oxygen
Fossils of soft bodied,
complex animals
Animals with exoskeletons
Oxygen reaches values near
modern levels
Dinosaurs begin development
Pangaea all together
65 Million
Dinosaur extinction, mammals
begin rise
~5 Million
Earliest known fossils of
Human branch
Last major glaciation
10,000
Chapter 10
Evidence
Expansion of Universe as seen in redshift
of galaxies and quasars
Magnesium 26 ( the decay product of
Aluminum 26) is found in grains in
meteorites,
Other stars are seen forming in gas
clouds
Radioactive dating of Rocks,
Computations of Solar Evolution
Stromatolites and blue green algae fossils
found
Scratches on Rock Faces, Radioactive
Dating, and Strata of remaining rocks
Banded Iron found, Radioactive Dating,
and Strata
Burgess Shale
Fossils found
Oxidation levels in rocks, radioactive
dating of embedded fossils
Fossils and radioactive dating
Fossils indicate shorelines, radioactive
dating, magnetic fields in rocks show
alignment of continents
Iridium in dark rock layer. Above layer
many species become extinct. Ages from
radioactive dating.
Earth, Our Point of Reference
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143
Chapter 11 Comparative Planetology
As we think about the planets in our solar system, it is worthwhile to compare and contrast their
features. To do this, we will be dividing them into obvious big categories. As a start, we can deal
with the Terrestrial Planets and our Moon, Jovian Planets, and Icy Moons.
Terrestrial Planets and Earth’s Moon all have densities indicative of rock or rock and an iron
core. They all have solid surfaces that have been at least partly resurfaced since the objects were
formed. As we compare and contrast the surface features of these objects, it is useful to examine
both what they have and why they might be the same or different’
Earth
Moon
Mercury
Venus
Mars
Atmosphere
Folded Mountains
Magnetic Field
Plate Tectonics
Active Volcanoes
Water (running?)
Sedimentary layers
Impact Craters
Resurfaced
after
formation?
Iron Core
Valleys?
Cause(s) of
valleys
As we compare the terrestrial planets, we think that all of them have experienced collisions and
formed craters, but today they don’t all have the same number of craters. Venus is partly protected against impact craters by its thick atmosphere, as is Earth to a lesser degree. Craters
on Venus, Mercury and the Earth are covered over by lava flows and on the Earth are eroded by
the wind and weather. Some parts of Mars are covered with loose soil, so we don’t know anything about what might be below.
We think that all these terrestrial bodies started out hot, both from impacts releasing kinetic
energy and from radioactive decay. Their own gravity compresses them and heats then further.
Early in the histories of these planets, the heat was sufficient to melt each of these objects and
allow its densest materials to sink to the center. As time goes on, heat from the planets’ interiors works its way out. Radioactive decay continues, but the overall rate of energy released decreases
as radioactive nuclei decay into stable ones. Small objects like the Moon, asteroids and possible
Mars have had enough time to solidify all the way through. Once the object has completely
solidified, we do not expect to see volcanic events or new folded mountains. You might call these
cooled off bodies “dead”. Earth and Venus are so large that their interiors are still molten.
Some terrestrial objects have atmospheres. We are not sure about the source of gas for these
atmospheres. Some elements, like hydrogen and oxygen, can come both from within the
refractory original materials and from impacts by icy bodies like comets. Even when no crater is
formed, the materials from small meteors and comets can be accreted and incorporated into the
mass associated with the planet or moon. As you read this, there are many tiny meteors hitting
the Earth. They are stopped by our atmosphere, but they bring us material without leaving any
crater.
Even if all the terrestrial objects once had atmospheres, they don’t all have gas today. Whether an object can hold onto an atmosphere depends on whether the individual atoms or molecules of
gas reach escape velocity. Escape velocity comes from the same formula you have already
Chapter 11 Comparative Planetology
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144
learned,
Ve sc ape
2G(m1 m2 )
. Here one of the masses is the mass of the planet, and
r
the other is the mass of the atom or molecule. The distance is the distance from the center of the
planet or moon to the molecule. The mass of the molecule is definitely negligible compared to the
mass of the planet. But the mass of the atom or molecule matters a lot determining whether it will
HAVE the velocity escape.
Temperature measures the energy of random motion of free particles, like those in an
atmosphere. The higher the temperature, the higher the average kinetic energy, but all different
types of motion have the same average kinetic energy.
As you have learned, kinetic energy is given by the formula KE
1 2
mv . Since the average
2
kinetic energy of motion for every molecule is the same, the more massive molecules have
smaller velocities. The less massive ones move faster.
Which is the most massive molecule N2, CO2, H2O, or O2? To decide, you add up the masses of
the atoms (one unit for each proton or neutron) in the molecule. For CO 2 you would have one
carbon atom at 12 units, and 2 oxygen atoms at 16 units each. That is a total of 44 units, making
it the most massive of these molecules. Since CO 2 is the most massive, it will usually have the
lowest velocity and be less likely to escape. Water vapor has mass only 18 units, so it would have
a higher velocity than the other molecules and be more likely to escape. The average velocity
does not need to exceed escape velocity for a gas to escape eventually. Some of the molecules
have higher than average velocity and others lower. The highest velocity molecules can escape
even if the average velocity molecules cannot.
Mercury, the Moon, and Mars have small masses and have the least success retaining
atmospheres. Mars, being the most massive and the coldest, has retained some of its
atmosphere. The Moon and Mercury have nearly nothing.
In the case of Earth and Venus, both have extensive atmospheres, but Venus has over 90 times
as much total gas as the Earth. How did this come to be?
We think that the terrestrial planets started with some hydrogen and helium from the solar
nebula. Some of these gasses would have been attracted as the planets formed. But both
hydrogen and helium are very light molecules and largely escape.
Volcanoes on Venus, Earth and Mars probably create secondary atmospheres. Based on current
measurements, volcanoes expel water vapor (mostly) and carbon dioxide, as well as melted rock.
These eruptions lead to atmospheres with lots of water vapor and some carbon dioxide.
Venus’ high temperature probably caused water vapor to rise to the top of the atmosphere where
the molecules were broken up by ultraviolet light from the Sun. The hydrogen atoms could easily
escape at the high temperatures in Venus’ atmosphere. Venus’ atmosphere may still have the bulk of the carbon dioxide that has ever been expelled by its volcanoes.
As we know, water can exist as solid, liquid or gas on Earth’s surface. The large amounts of water vapor from volcanoes condensed to form oceans early in our history. Much of the carbon
dioxide dissolved in the oceans and some of the carbon was used to make seashells. The carbon
in the shells didn’t necessarily return to the atmosphere. The shells get compacted to limestone and removed from the atmosphere. In some cases plate tectonics drag the limestone (with its
carbon) back into Earth’s interior. Estimates of the total amount of gas above that has EVER
been part of Earth’s atmosphere indicate amounts comparable to the amount that Venus has. We think that the Oxygen molecules in Earth’s atmosphere are at least partly the result of life. Oxygen molecules (O2) react readily. If it were not always being renewed by plants and bacteria,
Chapter 11 Comparative Planetology
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145
we expect that the oxygen would react with the surface and would no longer be present in the
atmosphere.
The mass of Mars is only about 11% as large as Earth’s and its radius is about half as large.
Combining these effects, the escape velocity leads to an escape velocity only about 47% as large
as on the Earth. The lower temperature at Mars’ distance helps it to retain some of its atmosphere.
Jovian planets are distinguished by the predominance of gases and volatiles in their makeup.
Starting with Jupiter and progressing to Neptune, they progress from Jupiter with nearly solar
abundances of the elements to Neptune with decreasing percentages of hydrogen and increasing
percentages of rock and ice.
As we go further out in the solar system from Jupiter’s distance, the total amount of material in the original gas cloud seems to have decreased, resulting in less massive planets. Due to the
lower total masses, highly compressed forms, like metallic hydrogen are not found in Uranus and
Neptune.
All of the Jovian planets except Uranus have substantial amounts of internal energy. Jupiter, for
example, produces nearly twice as much energy from its hot interior as comes from the Sun. We
expect that Jovian planets will all have internal heating due to gravitational compression. Why
Uranus does not show more heating is the open question. (There probably isn’t a large enough percentage of radioactive materials in the cores of these planets to cause substantial heating),
Icy moons of Saturn and Uranus seem to form a family of icy-rocky bodies. This family may
include some of the smaller moons of Jupiter and of Neptune, but we do not yet have enough
information about their surfaces or compositions. The family certainly includes Mimas, Enceladus,
Tethys, Hyperion, Ariel, Umbriel, Titania and Oberon. It probably includes Rhea, Dione, and
Iapetus.
These moons show varying numbers of impact craters on surfaces largely composed of ice. The
surfaces typically have parts with few craters. These are probably places where the surface has
been cleaned up by out flowing water. They typically have areas that look like cracks or
riverbeds. Probably their surfaces have cracked open and allowed water to flow out, covering
over the earlier craters. These moons are probably not hot enough to melt rock and cause
volcanic flows with magma. Since the water stands in lieu of the melted rock, these processes are
often called icy vulcanism.
3
All of these icy-rocky moons have densities between 1 and 2 g/cm , indicating that there is a
large percentage of ice. Other moons, like Ganymede and Callisto probably have a larger
percentage rock than do some of the moons that are more distant from the Sun. Miranda shows
signs of icy vulcanism, but the surface includes such different large landforms, that there is more
going on than on other moons.
Questions (Read the textbook and come to lecture. Fill in the table at the start of the chapter to
solidify your knowledge, then try the questions)
1) You want to visit a moon where you can see craters more than 4 billion years old. Where could
you go? (There are lots of possibilities, see how many you can name)
2) What causes planets to have (ever) melted and allowed the denser materials to fall to the
center?
3) What objects have atmospheres? Why don’t all objects have them?
4) Where should you look for active volcanoes?
5) Aren’t all planets and moons made of the same elements? If that is so, what causes some objects to have active volcanoes and others to have none?
6) Are all the Jovian planets the same except for mass? If not, what is different?
Chapter 11 Comparative Planetology
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Astro 110
Test Review # 1
General, All Tests
Using your textbook and Handouts
The lectures and notes are primarily facts or techniques which are not in the textbook. So don’t
count on going home to read the book afterward to get an explanation. The information in the
notes is a required part of the course. Where there are blanks, they are meant to be filled in
during class. If you go home without filling in the blanks, you will have difficulty later.
These printed notes are designed to be in a loose-leaf notebook. Bring paper for the notebook to
class, As we go over material in class, either write directly on the handout, or place notebook
paper between the printed pages and take MORE notes right there. Taking notes helps us pay
attention. If something is unclear, it is even more important to take notes (and ask questions
immediately). Without notes, there will be no way to know what it is that is bothering you.
ASK QUESTIONS! as soon as possible. It helps everyone. It may seem that all the others think
that class is totally trivial, but many students are just sitting being shy and not understanding.
Often there is some other way to examine an issue, and you are the only one who has thought of
it. You will be contributing to everyone’s understanding.
After class, but before the next class, go over your notes and rewrite the information in your own
words. Do the problems. Do the homework as soon as we cover the material. The USUAL thing is
that material that made sense in class won’t be clear. At the start of every class, I will ask if
people have questions. That is the time to straighten out any problems.
The textbook material expands on and backs up what we do in the class during the first part of
the course. It should supplement, not supplant, your notes. It also has material about the stars
and planets that is not in the workbook.
Practice Questions
Our online class management system has practice questions for tests and quizzes. It is definitely
worthwhile to use it to practice. Practice versions of all assignments should be available all the
time. Please use them. When you have answered the questions, you should look at the answers
to see what to improve.
There are some differences between the online questions and the in person ones.
Quizzes might ask you to write definitions, to convert numbers, draw on the star map, draw a
diagram, like the Earth with the horizon, explain retrograde motion or circle things on a star map.
None of these is possible with the online version.
Online questions include matching, questions with several answers, more than five choices for
answers that are unlikely to be on the test. Online numerical answers are VERY picky about
format, number of significant figures etc. In person will not be so picky.
If there are numerical answers to choose among for a test, they will be chosen to ensure that the
correct method was used. But the value may not be the identical with yours, due to round off
errors or imprecision in reading a map. I will try not to make them very close together, but I will
include the results of common errors. Be prepared to choose the best one.
Scratch paper and conversion factors will be provided. You provide the scientific calculator and
brain.
Test 1
Test 1 will include Castle chapters 1- 5 in Castle and the corresponding material in your textbook.
Chapter 1
I will not ask you to memorize the exact sizes. I may ask you which is the larger of two things or
what the relation between two things, e.g. is the Solar System part of the Milky Way or the
reverse.
Astro 110
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I would ask you to plot a value on the logarithmic scale, or I might ask you some information
which you could read off the logarithmic plot. For example, what is the distance from the Sun to
Pluto in kilometers? How many times as large as the Astronomical Unit is the distance to the
nearest star? (count powers of 10 from the chart)
You might be asked to convert a value. You would be provided with the information about what to
convert and any conversion factors which you need. For example, ”The distance between two
spiral arms is 3 kpc, plot this distance on the logarithmic plot”. You would be given the fact that a
13
parsec is 3.09 x 10 km and probably the fact that kpc means kiloparsecs, i.e. thousand parsecs.
Key Terms celestial equation, crescent phase, declination, diurnal, ecliptic, equatorial system, full
phase, gibbous phase, meridian, new phase, nodes, north celestial pole, circumpolar, quarter
phase, right ascension, summer solstice, tropical year, vernal equinox, waning crescent, waxing
crescent, winter solstice, year, zodiacal constellation. The terms prograde motion, retrograde
motion will be in test 2.
Ch 3 precession pp 49-50
Understand what precession means for the motion of the Earth and for its effects on the identity
of the north star. Understand how the tropical year changes what part of the Earth’s orbit
corresponds to winter in order to keep the seasons and the months the same in spite of
precession. (in class mostly).
Chapter 2 Constellations:
You should be prepared to find and identify those constellations we have covered and only those.
You may be asked to find these constellations on either the polar (round) map or the all sky
mercator projection maps (rectangular). These will be the maps without lines as shown in ch
2 of Castle. I will provide little marks at the edges of the mercator projection to indicate
where the declination and Right Ascension lines would be. They will not be labeled. I expect you
to remember what direction the values go and what numbers go at each mark. On a test, you will
have scratch paper, but you will be asked not to write on the map itself. On a quiz, you will be
able to write on the map.
Know the official name of the constellation (in Latin), what the constellation is supposed to
represent, and the name(s) of any first magnitude stars in the constellation. Be prepared to find
tell what constellation a star is in and what its Right Ascension and declination are (read from
map).
You will not be required to draw the shape of any constellation or to describe the myth. You
should be able to find the constellation or any of the named stars on the map and to read off the
approximate Right Ascension and Declination from the map. There is no need to memorize the
numbers unless you prefer.
I might put a letter on a constellation and ask for the name, ask you to circle the constellation. I
might ask you to label the star or name the labeled star, or to tell what the constellation is
supposed to be. These questions are so pictorial and so straightforward that they do not appear
in the test review in any detail.
Study Suggestions for the Constellations – I suggest that you make lots of copies of the blank
sides of the star maps. Each time we study constellations, review the constellations, and practice
filling in the maps. Draw and label everything. When you can do no more, look on the filled in map
and finish. Don’t stop with filling in the map once, fill it in several times for each class day. Do it
until you can fill in all the constellations we have studied. Then do it again the next class day.
Ch 3 How Earth and Sky Work- Effects of Latitude
Be able to relate the latitude of an observer, the range of declinations which the observer can
see, the range of declinations which are circumpolar. Be able to find the observer’s latitude when
given any of the following:
Astro 110
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148
-the altitude of the North Celestial Pole
-the fact that a certain star is circumpolar but none further from the pole is,
-the extreme south or north declination the observer can see
Be able to define terms like right ascension, declination, latitude, altitude, meridian etc.
Ch 4 How Earth and Sky Work -The Effect of Time
Given any two of the following, you should be able to find the third:
Sidereal time (what is on the meridian)
Solar time
Date
The problems will be written in a variety of forms.
There are also simpler problems, such as finding the sidereal time when given the constellation
on the meridian.
Ch 5 Positions of the Sun and Moon
Be able to find the Right Ascension (accurate to one hour) and declination of the Sun given the
date. If asked to find what constellation the Sun is in, you should be able to look on the map and
find it (assuming that it is one of the ones we have studied).
Understand how the rise and set points of the Sun change as a function of the seasons.
Understand what precession is, why the pole star and coordinates of stars change as a result of
precession, and what causes precession.
Be able to explain the motions and phases of the Moon.
Given a picture of the earth, the Sun, and the Moon, you should be able to determine the phase
of the Moon, or draw the same picture given the phase. .
Understand how long it takes for the Moon to orbit the Earth. Be able to predict when the next
occurrence of a given phase of the Moon will occur, given the date of a particular phase (for
approximately one month forward or backwar
Know what time of night each phase of the Moon rises and sets for an observer at the equator.
Calculate the Right Ascension of the Moon given the phase and the date.
Describe why and when there are eclipses. Know the names of the phases of the Moon and at
what solar times they can be seen).
Understand the geometry of lunar and solar eclipses. Be able to predict roughly when an eclipse
is possible, given the date of another eclipse.
Example Questions:
1) What is the range of circumpolar star positions found from Vancouver, B.C. at about +50o?
a) Cannot tell from the information given
b) +90o to +40o
c) +90o to -40o
d) +90o to +50o
e) +90o to -40o
2) What is the furthest north that the Large Magellanic Cloud, one of our companion galaxies, at
declination -70o can be seen? a) 0o
b) 70o c) -70o
d) 20o e) -20o
3) If Deneb is on the meridian and it is 9 PM, what date is it?
a) Mar 21
b) June 21
c) July 21
d) Aug 21
e) Sept 23
o
4) If you see the North Celestial Pole at altitude 14 , what is your latitude?
o
o
o
o
b) 66
c) cannot tell
d) 76 e) 90
a) +14
Astro 110
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149
5) If you can see Castor just barely come above the horizon at culmination (its highest point when
it is on the meridian). The rest of the time, Castor is below the horizon at your latitude. Where are
o
o
o
o
o
b) +58
c) +90
d) +-32
e) -58
you ? a) +32
6) When Betelgeuse is at the zenith, what is your latitude?
o
o
o
o
b) +27
c) 0
d) +83
a) +7
e) -25
o
7) When you are at +30 latitude, the range of declinations which is circumpolar is
o
o
o
o
o
o
a) From +30 through -30 b) From +90 through -30 c) From +90 through +60
o
o
o
o
+90 through 30 e) From -90 through 30
d) From
8) You can see Rigel as circumpolar, but everything further north is not circumpolar. What is your
o
o
o
o
o
b) -8
c) 0
d) 8
e) -82
latitude?
a) +82
9) The distance to the nearest star is 1.3 parsecs, how many kilometers is that?
7
8
13
24
a) 1.3 km b) 6 x10 km c) 1.95x 10 km d) 4. x 10 km e) 1x10 km
10) What is the relationship between the Jupiter and the Earth?
a) Jupiter orbits the Earth
b) The Earth orbits Jupiter
c) Jupiter is part of the Earth
d) Jupiter is part of the Solar System and the Earth is part of the galaxy e) They both orbit the
Sun
11) On December 21, you would like to observe Regulus. What time will it be on the meridian?
a) 6 AM
b) 4 AM
c) 2 AM
d) Midnight
e) 10PM
o
12) If you are at latitude 20 what is the range of declinations which you can see?
o
o
o
o
o
o
a) From +20 through -20 b) From +90 through -20 c) From +90 through -70
o
o
o
o
e) From -90 through -70
+90 through 20
d) From
13) What is the Sidereal Time on May 6 at 1 PM?
a) 4 hr b) 9hr c) 15 hr d) 1 hr e) None of the above
14) What is the sidereal time at 8AM on Nov 6?
a) 9 hr b) 11hr c) 4 hr
d) 8 hr e) None of the above
15) Which configuration below shows an observer at 10 PM?
e) Cannot tell
from the information
16) What is the sidereal time on May 31 at
3AM?
a) 13 hr
b) 4 hr c)8 hr d) 20 hr e) Cannot
tell from the information
17) What is the declination of the Sun on May 6?
a) Cannot tell b) 0 deg
c) 23.5 deg
d)
17 deg e) -17 deg
18) What is the declination of the Sun on Feb 6?
a) Cannot tell
b) 0 deg
c) 23.5 deg
d) 10 deg
e) -16 deg
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19) Which position of the Moon as shown in the figure is first quarter?
20) Which position of the Moon (as shown in the following figure) is waning gibbous?
21) In the figure from # 20,
which of the lunar positions is on
the meridian at midnight?
22) In the figure from #20, which
of the lunar positions is on the
Eastern horizon at 4PM?
23) If I see the crescent Moon at
3AM and I am near the Earth’s
equator, is it?
a) waxing
b) waning
c) could be either
24) If it is new Moon on Tuesday,
September 4, when is third quarter?
a) October 4
b) September 11
c) September 19 d) September 25 e) Cannot tell
25) If it is full Moon on Tuesday, September 11, when is new Moon?
a) October 2
b) September 4 c) September 19 d) September 25 e) Cannot tell
26) If it is first quarter Moon on Tuesday, September 11, when is next opportunity for a solar
eclipse?
a) October 2
b) Sept 4 c) Sept 19 d) Sept 25 e) Cannot tell
27) If it is first quarter Moon on Tuesday, September 11, when is next opportunity for a lunar
eclipse? a) Oct 2
b) Sept 4 c) Sept 19 d) Sept 25 e) Cannot tell
28) If it is October 7 and Orion is on the meridian, what time is it?
a) Midnight
b) 9PM c) 9AM d) 4AM e) 3PM
29) What constellation is at 15 degrees Declination 11 hours Right Ascension? (hint use the
map) a) Orion
b) Draco
c) Ursa Minor d) Virgo
e) Leo
30) Which letter identifies Deneb on mercator map? (example question, map not supplied. You
would have the map to look at, but you will need to find Deneb)
31) What constellation is Regulus in?
a) Draco
b) Orion
c) Canis Major
d) Bootes
e) Leo
32) If there is a solar eclipse on April 1, which of the following is a possible date for another solar
eclipse?
a) April 10
b) May 10
c) Sept 19
d) July 10 e) Dec 8
33) If there is a total solar eclipse, the following is true
a) Everyone on the Earth will see it
b) Only one person will see it
c) Only people within 135 miles of the center of the shadow will see a total eclipse
d) The eclipse will last all day
e) It will occur at full Moon
34) What is the summer solstice?
a) Religious festival b) The highest point that a star
reaches as it goes across the sky c) The date when the Sun is furthest North d) The time when
there is most probability of an eclipse e) Mar 21
35) What is the major cause of the seasons on the Earth? a) Changes in the distance from the
Sun b) The tilt of the axis changes in space over the year
c) Changes in the thickness of
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the atmosphere d) The tilt of the axis stays the same in space, but changes compared to the Sun
e) The pole star changes
36) What is one effect of precession? a) Weather changes
b) Pole star changes
Distance to Sun changes
d) Nothing
e) The Earth will fall over
c)
37) If it October 7 and the Moon is Waning Gibbous, what is the Right Ascension of the Moon?
` a) 1 hour
b) 4hr c) 6 hr d) 23
hr
e) 6 hr
38) What is the time in the following picture?
The Sun is on the front surface of the picture
a) 9AM
b) 5PM
c) 7AM
d) Noon
e) Midnight
39) What is Auriga supposed to be? a) The
Little Caesar’s man
b) A king, Auriga is his
name
c) A charioteer d) A herdsman
e) A dog
40) The best choice for the coordinates of Aquila would be
o
o
o
o
b) 19hr 0
c) 6hr 0
d) 21 hr 40
a) 19hr 40
e) 12hr 10
o
41) What is the difference between Right Ascension and sidereal time?
a) There is none, they are synonyms
b) The Right Ascension is on the Earth, sidereal time is on the sky
c) The Right Ascension measures north-south position, sidereal time measures which way the
guy’s head is pointing
d) The Right Ascension tells the position of a body on the celestial sphere, the sidereal time tells
which direction the meridian is pointing
e) The sidereal time tells the position of a body on the celestial sphere, the Right Ascension tells
which direction the meridian is pointing
42) In what constellation would you find Aldebaran?
a) Orion
b) Scorpius
c) Aquila
d) Taurus
e) Lyra
Answers 1b, 2 d, 3 e, 4 a, 5e, assuming that Castor is at +32 degrees, the latitude will be 90o
different, 6 a, 7 c, 8 e, 9 d, 10e, 11b, 12 c, 13a, 14b,15b, 16d, 17d, 18e, 19b, 20c, 21e, 22d, 23b,
24d, 25d, 26a, 27c, 28d, 29 e, 31e, 32 slightly less than 6 months later c, 33c, 34c, 35d, 36b,
37b, 38 b Remember that the Earth spins causing celestial bodies to appear to rise in the East,
cross the meridian at culmination, and set in the west. In the case of the Sun, the meridian
crossing is noon. The time before meridian crossing, when the Sun is in the East is AM, and after
meridian crossing the Sun is in the West and it is PM. At best one can estimate the time from how
close to the meridian or the horizon the Sun appears. Be sure to note whether the Sun is in the
front or back of the figure. The instructions will specify. 39c, 40b (you can tell from the map, it is
not necessary to memorize the numbers), 41d, 42 d
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Astronomy 110 Test 2 Review Castle Chapters 6, 7, and possibly 8
NOTE: THIS IS NOT MEANT TO BE EXHAUSTIVE, THIS IS TO HELP THE YOU TRAIN
ON THE QUESTION FORMATS AND THE CONCEPTS. Just because an issue is mentioned
here does not mean that it cannot be on a test. WebCT has practice quizzes and tests for your
use. There are also separate practice quizzes to help you train on using laws and formulae.
Ch 6 History of Astronomy
Summarize the apparent motions of the Sun, the Moon and the planets and present day
explanations of these phenomena in both today’s and historical models of the Universe. There is
a table at the end of chapter 6 to show all these items.
Be able to explain retrograde motion in both the current and Ptolemy’s models. You are likely to
get an essay question on a quiz concerning these.
Understand the apparent paths of the Sun as it rises and sets on different days of the year.
Similarly picture the path of the Moon and the way it changes over the cycle of the lunar nodes.
Know about archeoastronomy sites including Fahade Butte (the Sun Dagger), Mayan sites and
Stonehenge. Know roughly when they were constructed, what they look like, what they are
aligned with, and where they are located.
There is a sequence of historical figures and their models. You can be asked about any of these.
It is good to make yourself a 3 x 5 inch card for each person, write out the key features of the
model, the dates and books and the person’s life. Then study the information.
Be aware of each of the Greeks, what they did and how their models worked. Understand the
contributions of the Islamic world, Copernicus, Brahe, Kepler, Galileo and Newton. Know how
each model worked. Understand what the models did and didn’t predict, what their features are
for. Do not worry about the modern parts of the history outline (after Newton). These are just to
provide you with background information.
Think about the ways that Eratosthenes and Aristarchus measured things and be ready to explain
them. You won’t have to do any math, but you should be able to explain what will happen if the
distance to the Moon were greater, or the distance between Alexandria and Syene.
Be able to assess how each of the geocentric and heliocentric models explains rising and setting,
motion of the Sun, motion of the planets.
Be aware of what happened to Galileo and why. Understand why people did or did not believe in
Copernicus’ model.
I would ask you the date when someone lived or who wrote a particular book. It would be multiple
choice.
Kepler’s three laws are in chapter 6. You are expected to know what each one says and how to
use Kepler’s third law to find P or find a, if given the other. You will also need to know the
features of an ellipse (e.g. focus, major axis, semimajor axis, aphelion, perihelion etc).
Be able to distinguish a correct vs. an incorrect ellipse, and distinguish whether the foci are in the
correct place. Be able to determine where a planet would go the fastest in its orbit. Be able to
draw and label the major and minor axes of an ellipse. You should be able to find the period of a
planet given the semimajor axis of the orbit around the Sun, or visa versa.
Ch 7 The Start of Modern Physics -Using Equations and Formulae
Newton and Kepler formulated laws that you will be using. There is a table at the end of chapter
7. It is meant for you to organize these laws and their uses. Fill it in and go over the practice
problems at the end of chapter 7 to train yourself on how to decide what equation is needed for
each type of problem.
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Appreciate the difference between Newton's Laws, which predict additional phenomena, and
Kepler's laws or Ptolemy's epicycles which only describe the phenomena. Your book includes
the formulae for circular and escape velocities.
Be able to calculate the circular and escape velocities, how to find weight on other planets, and to
solve linear momentum problems.
Understand what escape velocity means.
Understand the definition of a black hole and what would cause one (there is more than one way,
and more than one size). Understand the way that we detect black holes.
Summary
Things to Remember:
The apparent motions of celestial objects (like stars, Moon etc), how often they repeat,
and how each model explains their occurrence
Explanations for retrograde motion
Use of parallax and implications when it is not detected.
Kepler's and Newton's laws
Defining features of an ellipse
Meaning of momentum
Law of Gravity
Formula for speed in a circular orbit, and for escape velocity
What Galileo discovered, and the significance of each major observation
Cosmologies of the various Greeks, Copernicus, Kepler, Galileo, Newton
Ptolemy’s purpose for the Epicycle, Deferent and Equant
When various people lived (at least the order and the century)
How various solar and lunar calendars work
H-1 Match the beliefs with all the people who held them. They are NOT one for one. The point is
for you to look these up and summarize, so the answers are not included.
a) Spherical Earth
1) Copernicus
b) Crystalline spheres
2) Aristotle
c) Counter rotating spheres
3) Kepler
d) Disk like earth or planet
4) Hipparchus
e) Elliptical Orbits
5) Anaximander
f) Rotating Earth
6) Tycho Brahe
g) Epicycle
7) Ptolemy
h) Geocentric Universe
8) Anaximenes
i) Cylindrical Earth
9) Eudoxus
j) Primum Mobile
10) Thales
k) Heliocentric Universe
11) Anaximenes
l) Equant
m) Firmament
H-2 What supports the solid part of the Earth, according to Thales?
H-3 Why did the Greeks think that the Earth is a sphere? That is, what is the evidence that they
found and the logic they used?
H-4 How did Ptolemy explain the mechanism which makes the stars rise and set?
H–5 What causes the cosmos to move in Aristotle’s model?
H-6 Why did the Sun move through the constellations according to Ptolemy:?
H-7 What alignments would you find at Stonehenge? When was it built?
H-8 What is the major contribution of the Babylonians to the development of modern astronomy?
H-9 How does Ptolemy’s model explain the “irregularities of the motion of the planets,” that is they
do not progress at a constant speed through the sky (different from retrograde motion). How
does Copernicus’ model explain it?
H–10 What does retrograde mean?
H–11 Parallax was not observed until 1838. How did the fact that it was not observed affect the
models which Tycho Brahe and Aristotle suggested?
H-12 How did Eratosthenes measure the size of the Earth?
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H-13 What measurements did Aristarchus use to measure the distance to the Sun?
H-14 What book did Copernicus write to document his theory?
H-15 Why did Kepler give up on the idea of circular orbits? What did he use instead?
H-16 What is the deferent? Be able to find it on a diagram of a solar system model.
H-17 Who discovered precession?
H-18 Where did Anaximenes believe that the Sun and Moon go at the end of the day?
H-19 When did Aristotle live?
H-20 What did Galileo discover which was direct support of the Copernican model?
H-21 What are perfect solids? Why did Kepler use them ?
H-22 What are Kepler’s three laws?
H-23 What did the Islamic world do with Ptolemy’s model? What did they rename his book?
H-24 What measurements did Aristarchus use to find the size of the Moon?
H-25 If you were to discover a medicine wheel, what would you be looking at? Where
(geographically) are you likely to be?
H -26 You want to build an artificial satellite of the Sun. You want it to have a period of exactly 5
years. What will the semimajor axis of the orbit of the planet be?
H -27 An asteroid is found to have a semimajor axis of 32 Astronomical Units. How long will it
take to orbit the Sun?
H–28 You want to launch a vehicle which will orbit the Sun, and return to the vicinity of the Earth
in 64 years, what will the semimajor axis of its orbit be? (the orbit can be any elliptical shape you
want and it can pass by the Earth when it is near the Sun).
H–29 Draw an ellipse and label the foci (plural of focus), the major axis, the minor axis, and one
semimajor axis.
H–30 Is it physically possible for a planet to orbit the Sun in a circle? How does this correspond to
Kepler’s first law?
H-31 Where is Fahade Butte? What sort of construction is there? What is the name of the people
who we believe built it? What astronomical alignments are there?
H–32 What kind of calendar did the Egyptians use?
H-33 If you notice a comet and find that its orbit has a semimajor axis of 64 Astronomical Units,
what is its period in orbit around the Sun?
H-34 What is the difference between the Julian and the Gregorian calendars? When was each
brought into use?
Gravity and Motion
Understand the definition of a black hole and what would cause one (there is more than one way,
and more than one size). Understand the way that we detect black holes.
Example questions concerning physics etc.
P-1 You are batting and a batting machine is pitching to you. If the machine is fed with both tennis
balls(light) and hard balls (heavy). If you can’t tell between the balls when you see them, how else
could you tell which is which? (the pitching machine is not adjustable, it puts the same force on
the balls as it lobs them at you)
P-2 You are playing pool. The table looks like
the picture below. The 5 ball is hit by the pool.
The 5 ball has mass 3 times that of the 9 ball .
What could happen to the balls?
a) The 5 ball will bounce off the 9 ball and
reverse direction. The 9 ball will remain
stationary.
b) The 5 ball and the 9 ball will move in the
same direction and with the same speed that the 5 ball had originally
c) The 5 ball and the 9 ball will move in the same direction that the 5 ball was originally going.
The 5 ball will move more slowly than it was previously. The 9 ball will move faster than the 5 ball
after the collision.
d) The 5 ball and the 9 ball will move in opposite directions at the equal speeds e) The two balls
will both move off at right angles to the direction which the 5 ball was moving
P-3 Name three quantities that are conserved in physics.
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P-4 When you fire a gun, the bullet comes out the front with velocity V. The gun
a) Stays there
b) Tries to move backward as fast as the bullet went out (but your hand stops it)
c) Tries to move backward, more slowly than the bullet went (but your hand stops it)
d) Tries to move in the same direction as the bullet, but more slowly than the bullet went. (but
your hand stops it)
e) Tries to move toward the floor
P-5 What principle would you use to describe the motion of the gun (in the preceding problem)
when you fire it?
a) The law of gravity
b) Conservation of energy
c) Conservation momentum
d) Newton’s first law
e) Kepler’s second law
P-6 When you see a comet near the Sun, the speed it will move can be predicted by (more than
one answer)
a) Kepler’s first law
b) Kepler’s second law c) Newton’s first law
d) Kepler’s third law
e) Conservation of angular momentum
P-7 You are playing tether ball and the ball is winding up the pole at the very end, it moves very
fast. This is an example of
a) Conservation of energy
b) Conservation of linear momentum
c) Conservation of angular momentum d) Kepler’s third law
e) Law of gravity
P-8 You carry a chicken and a bathroom scale (the kind with springs) to the top of a very high
building. You expect
a) The chicken will get air sick b) The chicken will weigh more
c) The chicken will weigh less
d) The chicken will become lighter than air and float away
e) You will all become weightless.
P-9 If you are in the space shuttle, you might say you are weightless. Is this because
a) The gravity of the Earth only goes as far as the atmosphere
b) The gravity goes only a few miles above the surface of the Earth, regardless of whether there
is air
c) Gravity accelerates the shuttle more than it accelerates you, so you seem to float away from
the shuttle
d) Gravity accelerates you and the shuttle the same, so you seem to float
e) You are so close to the Moon, that it pulls on you harder than does the Earth. So you do not
feel the Earth’s gravity.
P-10 What defines a black hole? What might cause one?
P-11 What does it mean to have escape velocity? What if you have less? What if you have more?
P-12 We think that the Universe is expanding. What do we think will determine whether it will ever
stop expanding?
P-13 How far from the Earth do you have to go so there will be no force from Earth’s gravity?
P-14 If you move further from a body, does the amount of velocity which you will need in order to
escape increase or decrease?
P-15 How fast is Pluto moving as it orbits the Sun? (look up the data you need from the book,
then compute)
P-16 If you wanted Mercury to escape from its orbit, how fast would it need to go?
How much faster is that than it is going now?
P-17 The Moon orbits the Earth and obeys the same laws as do the other planets. It moves at
about 1 km/sec in its orbit. How fast would it need to go to escape from its orbit and to leave the
vicinity of the Earth?
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P-18 What is the cause of tides?
a) Too much water
b) The earth's rotation c) The fact that the force of gravity decreases
with distance d) The Sun
e) Centrifugal force
P-19 How many high tides are there in a day at a given location? a) None b) One
c) Two d) Three e) Varies by season
P-20 If the month and the day were the same length, what would happen to tides?
a) They would get more extremeb) They would get less extreme c) There would be only one a
day
d) Nothing, they would be the same as they are now
e) They would stay at the same location on earth
Selected Answers History 26) 2.92 AU 27) 181.02 yr, 28) 16 AU, 33) 512 yr
Gravity and Motion P-1) heavy ball is more massive, but the force from the machine is the
same, so speed of the more massive ball will be lower and it will hit the ground closer to the
machine, P-2) c, P-4) c, P-5) c, P-6) b and e, P- 7) c, P- 8) c, P-9) d, P-10) use the speed of the
earth as it orbits the Sun and the circular velocity law to get about 4.8 km/sec, P-16) 68.5 km/sec,
P-17) 1.414 km/sec , P-18) c, P-19) c, P-20) e
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Astronomy 110 Final Review
There may be one or more questions which require that you identify a picture from among others.
Pictures could include planets, galaxies, comets, moons, etc There will NOT be subtle differences
like a crater on the Moon vs a crater on Mercury. On the other hand, you should be able to tell the
Sun from Mercury, or tell from Io from an elliptical galaxy.
There may be one or more “travel agent” questions. These are questions where you would be deciding among destination for travelers based on matching what they want to experience. You
might make a 3x5 card for each of the planets and the important moons, so that you can
summarize their features. Look at the matching list to see some of the important properties.
Check the last week of class to be certain of how far we get in the class. The final will start after
test 2. The final parts: stars, galaxies and the universe will be covered only briefly at best. The
lecture will summarize what you need to know about galaxies etc.
EARTH Castle Ch 10, Units 35, 36, 48
Have an overall idea of the age of the Earth, how the continents have moved and how life and the
atmosphere have evolved. I don’t stress the layers of the atmosphere or the types of rocks. I do stress landforms (mountains, volcanoes, lava flows) etc. in lecture and the relationship between
the Earth’s atmosphere and life. We will discuss radioactive dating using several elements (including Carbon 14, for previously
living material only). We will talk about daughter elements, the results of radioactive decay of
parent atoms (by fission). Be able to find the age of a sample given a plot of the amounts of
parent and daughter at different time. You will not need to memorize the half life of anything.
Understand the differences between convection, conduction, and radiation.
Earth questions (including radioactive decay and heat transfer)
E-1 The age of the Earth (based on geological evidence) is approximately
a) 10 Billion years b) 16 Billion years c) 4.5 Billion years d) 1 Billion years e) 10 Million years
E-2 The Earth’s atmosphere includes a substantial fraction of Oxygen. Is this the original composition of the atmosphere? If not, what was the earlier atmosphere?
E-3 Which of the following is evidence for a molten interior of the Earth?
a) Deserts
b) Rivers
c) Sandstones
d) Volcanoes
e) Glaciers
E-4 Plate tectonics is
a) Breaking and bending of plates
b) The science of ice ages
c) The science of
finding the ages of things
d) The motion of the divisions of the Earth's crust
e) The way in which mountains form from volcanoes and get worn down
E-5 The greenhouse effect is
a) A way of keeping plants from getting weeds
b) Destruction of the ozone layer by pesticides and fertilizers used in greenhouses
c)The way air circulates from the equator to the poles which keeps the poles comparatively warm
d) A method whereby carbon dioxide keeps the Earth warm by preventing radiation
e) A method for determining how old previously living things are based on the amount of carbon
they have
E-6 How long do we think there has been life on the Earth?
a) 1 Million years
b) 250 Million years
c) 500 Million years
d) 3.8 Billion years
e) 4.3 Billion years
E-7 Why do we think that the continents have not always been in the same place?
a) Because there used to be ice in the temperate regions
b) Because we can measure the motion
c) Because the surface of the Earth has been getting smaller as it cools, so the continents are
coming closer together
d) Because human languages are related, so we probably all came from the same location
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e) Because beaches and entire continents are getting washed away by hurricanes
E-8 What is the major constituent of the Earth's atmosphere?
a) Oxygen
b) Hydrogen
c) Nitrogen
d) Carbon Dioxide
e) Ozone
E-9 What is the most common land form on the earth?
a) Volcanic plains
b) Polar deposits
c) Cratered terrain
d) Volcanic constructs
e)Platform deposits
E-10How does the greenhouse effect work? How does it affect the planet’s temperature?
E-11 Why do we care about the Ozone in the Earth’s atmosphere?
E-12 What causes the Earth’s magnetic field, according to current theories?
E-13 How are most mountains on the Earth formed?
E-14 What is a P wave?
E-15 What evidence do we have that the center of the Earth includes molten material?
E-16 What causes the aurora?
E-17 When heat is transferred by radiation, what carries the heat?
E-18 When heat is transferred by convection, what carries the heat?
E-19 When heat is transferred by conduction, what carries the heat?
E-20 What do we think is the mechanism to carry heat within the core of the Earth?
E-21 What do we think is the mechanism which carries heat within the Earth’smantle E-22 What causes the motions of the continents associated with plate tectonics?
E-23 How old are the oldest stromatolites? What are they?
E-24 What is viscosity? How does it affect the shape of volcanoes?
E-25 What distinguishes between a valley made by a glacier from one made by a river?
E-26 What can be deduced from the density of the Earth or another planet?
E-27 What is hydrostatic equilibrium?
E-28 If you are examining a rock and find that there is 87.5% parent and 12.5% daughter, how
many half lives has it been since the rock formed?
E-29 What is the half life of the species shown in the figure below?
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1
0.9
P arent
Daught er
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.00E+ 00
2.00E+ 08
4.00E+ 08
6.00E+ 08
8.00E+ 08
1.00E+ 09
1.20E+ 09
1.40E+ 09
1.60E+ 09
T im e, years
E-30 How old would a rock be if it had 15% daughter and 85% parent of the radioactive species
in the figure above?
Earth’s Moon (Unit 37)
Moon-1) How thick is the Moon’s crust likely to be?
Moon -2) Why does the Moon have more craters than does the Earth?
Moon -3) What does a mare region consist of?
Moon -4) What are some differences between the side of the Moon facing Earth and the other
side?
Moon -5) Does the Moon have an overall magnetic field, as far as we know?
Moon -6) What is a rille?
Moon -7) What is a basin? How is it different from a crater?
Moon -8) What is the current theory of how the Moon formed? What argurments support this
theory?
Moon -9) Which is older, a mare region or a highland (terra) region? How do we know?
Moon -10) What can be told from the density of craters on a portion of the surface of the Moon?
Moon -11) What is the evidence for and against water on the Moon?
Venus and Mercury (Units 38, 39)
VM-1) How long is the solar day on Mercury? Why is it so different from the sidereal rotation
period?
VM-2) Has ice been observed on Mercury? How can it survive the heat?
VM-3) What is Ishtar Terra?
VM-4) What is Aphrodite Terra? What might have caused it?
VM-5) What is the Caloris Basin?
VM-6) Describe a scarp
VM-7) Which planet would you be most likely to mistake for our Moon if you were on the
surface? Why?
VM-8) Why are there few impact craters on Venus/
VM-9) What is an arachnoid?
VM-10) What is the reason that Venus is so much hotter than the Earth, according to current
theory?
VM-11) Mercury is very dense for such a small planet. What do we think has caused it to be so
dense?
VM-12) How is it possible for ice to exist on Mercury? What is the evidence is there for ice?
VM-13) Why is it that the day and night temperatures on Venus are so similar?
VM-14) The Magellan vehicle used radar to observe Venus. Why didn’t it use visible light?
VM-15) What is the evidence that there might be crustal motion on Venus?
Mars (Unit 40)
Mars-1) What is the evidence that there has been liquid water on the surface of Mars in the past?
Mars-2) What is the evidence that there cannot be liquid water on the surface of Mars at present?
Mars-3) Why does Mars appear especially red during the Martian winter?
Mars-4) What are the Martian polar caps made of?
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Mars-5) How are the Martian volcanoes different from those on the Earth and on Venus?
Mars-6) What is the weather on Mars like?
Mars-7) How would you distinguish between a run-off channel and an outflow channel?
Mars-8) How does the viscosity of lava on Mars compare with the viscosity of lava on the Moon?
Mars-9) If you wanted to find an impact crater on Mars, where would you look?
Mars-10) Does Mars have moons? What are they like?
Mars-11) What is the major constituent of Mars atmosphere?
Jupiter and Saturn (Unit 43,44)
We will talk about tidal stretching in class. Fix uses “Roche distance” for the distance where tidal stretching matches the internal gravitational binding of a moon. I call this the “Roche limit”. JS-1) What is the evidence that the rings of Jupiter and Saturn are not solid bodies?
JS-2) What is the evidence that Jupiter and Saturn generate substantial internal energy? Does
either generate more energy than they get from the Sun?
JS-3) What do we believe is the source of the internal energy of Jupiter and Saturn?
JS-4) Why are Jupiter and Saturn hot on the inside?
JS-5) Is the Great Red Spot a feature pinned to the core of Jupiter? How do we know?
JS-6) What is the indication of convection on Jupiter?
JS-7) What are Jupiter and Saturn made of?
JS-8) Where would you find metallic hydrogen? How is it different from the usual hydrogen gas
we are used to ?
JS-9) How do we come to have information about the internal layers of the Jovian planets?
JS-10) What makes Saturn’s rings so flat?
JS-11) What causes the spokes in Saturn’s rings? Why can’t they just be colored regions in the rings?
JS-12) What happens at the Roche limit? (or distance) What would happen to a body which
comes closer to a large body than this distance?
JS-13) Why is it that Jupiter’s rings appear brighter when sunlight shines through them, while Saturn’s rings are brighter when the Sun is behind the observer? JS-14) What does it mean to say that two bodies have orbits which are in resonance?
JS-15) What does the resonance do to their orbits?
The Outer Planets (Units 44, 45, 46)
I would not ask picky details of the discoveries of the planets. I might ask about the general
method used. I would not ask about previous theories of the planets’ internal structures, only current ones.
UNP-1) What causes the blue color seen on Uranus and Neptune?
UNP-2) What do we think the internal structure of Uranus and Neptune is like?
UNP-3) What are shepherding satellites?
UNP-4) How do Uranus’ rings appear different when seen in forward scattering rather than backscattering?
UNP-5) Which of the planets rotates retrograde? Which of their moons orbits the same direction
as the planets rotate?
UNP-6) What is the appearance of the surface of Pluto?
UNP-7) Why is it that we were not able to find Charon when Pluto was first discovered?0
Jovian Planets and Moons (Units 43-46)
JPM-1) What features are found in the atmosphere of the Jovian planets? ( e.g. rings, bands,
craters, spots)
JPM-2) How fast do the Jovian planets rotate?
JPM-3) Which of the planets emits more heat than they receive from the Sun?
JPM-4) How do Pluto and Charon differ from the Jovian planets? From the terrestrial planets?
JPM-5) What causes the gaps in Saturn's rings?
JPM-6) What makes us think that the rings are very flat?
JPM-7) What makes us think that the rings are younger than the planet itself?
Satellites Overview (U 45, 46)
You will not be expected to know every satellite that was in the travel brochure homework, but be
certain to be able to recognize the Phobos, Deimos, the Galilean satellites of Jupiter, Titan,
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Mimas, Miranda, Triton, and Charon, from their descriptions or their pictures. Be aware of the icy
satellites like Ariel, Enceladus.
Sat-1) How do we tell what satellites are made of ?
Sat-2) What do we think causes Io to have volcanic eruptions
Sat-3) Which of the satellites have evidence for ice on their surfaces? Water under the surface?
Sat-4) How do we know that Io has a younger surface than, say Ganymede?
Sat-5) Several satellites have craters and grooves on their surfaces. Which are they?
Sat-6) What is unique about Miranda?
Sat-7) Which satellite has geysers?
Sat-8) What does the presence of geysers indicate about the interior of a body?
Sat-9) When a satellite orbits a planet retrograde, what does it indicate about the origin of the
satellite? Was it formed with the planet?
Sat-10) What is likely to happen to the orbit of a retrograde satellite as a result of the tidal
Planets Overview The following are overview questions for all the planets.
planets-1) What is the density of the earth? Of the other terrestrial planets?
planets-2) What can we deduce from the density of the planets?
planets-3) What is the structure of a Jovian planet? How does it differ from that of a terrestrial
planet.
Match ( not one for one)
1) Mercury
a) Atmosphere
2) Venus
b) Craters
3) Moon
c) Lava Flows
4) Mars
d) Folded mountains
5) Earth
e) Rays
6) Jupiter
f) Rilles
7) Saturn
g) Scarps
8) Uranus
h) Metallic Hydrogen
9) Neptune
i) Iron core
10) Pluto
j) Icy surface
11) Deimos
k) Greenhouse effect
12) Io
l) Dust storms
13) Europa
m) Volcanoes
14) Ganymede n) Polar caps
15) Triton
o) Tidal lock between rotation and revolution
16) Mimas
p) Magnetic field
17) Enceladus q) Retrograde rotation
18) Phobos
r) Have satellites
19) Titan
s) Is a satellite
20) Charon
t) Has Water
21) Miranda
u) Has evidence of once having had water
Asteroids and Comets (41, 47 U41 prob 1;U47 probs 1,2,3,4)
AC-1) Widmanstatten figures are crystals of iron. Where do they occur? What do they indicate
about the history of the body?
AC-2) What are the three main types of meteors? Which is the most common in terms of the total
mass?
AC-3) What direction does the tail of a comet point? Why?
AC-4) What is the Kuiper Belt? What is the Oort Cloud?
AC-5) How long do comets survive?
AC-6) How do we tell what comets are made of?
AC-7) What determines the date of meteor showers?
AC-8) What causes Kirkwood gaps? What causes them?
AC-9) What is significant about a carbonaceous chondrite?
AC-10) What causes meteor showers?
AC-11) What is a meteoroid? How is it different from a meteor?
AC-12) How would you distinguish a comet from an asteroid, should you see one?
AC-13) If we were out near Pluto, could we see a nearby comet with a complete tail? Why or why
not?
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The Sun (U 49, 50, 51)
Sun-1) What is the source of energy for the Sun? How do we know?
Sun-2) Why is the corona hot?
Sun-3) What is the solar cycle? What changes over the solar cycle?
Sun-4) What will the (approximate) latitude of spots be in the year 2007? (see the Butterfly
diagram p406)
Sun-5) When will the next solar maximum be?
Sun-6) What is the Maunder minimum?
Sun-7) What do we think causes sunspots and solar activity?
Sun-8) How fast does the sun rotate i.e. what is its period?
Sun-9) What is the solar wind?
Sun-10) How does the latitude of a sunspots change over the course of a cycle?
Sun-11) What is the Butterfly diagram?
Sun-12) What is the source of energy for the Sun? Why do we think so?
Sun-13) How old is the Sun? How has its brightness changed?
Sun-14) How hot is the exterior of the Sun? The core?
Sun-15) Why do we expect a particular number of neutrinos from the Sun?
Sun-16) How do we explain the current number of neutrinos received?
Stellar Spectra, H-R Diagram, Masses of Stars (Units 58, 59)
Know the order of the spectral types, from hottest to coolest.
You will still need to remember the concepts of what an absorption spectrum looks like and the
idea of Doppler shift. Get the idea that more massive stars live a SHORTER time.
Be able to use a Hertzsprung-Russell diagram to look up the temperature of a star, or to find its
luminosity if given the luminosity class (the Roman numeral). Use the diagrams when answering
the questions below.
Stars-1) Why do some stars show only faint lines of hydrogen, when hydrogen is the most
common element?
Stars-2) What is the temperature of a B5 star?
Stars-3) What is the most common element in the Universe?
Stars-4) What is the evidence that Hydrogen is the most common element?
Stars-5) How can the rotational velocity of a star be found?
Stars-6) How many times as bright as the Sun would an F5II star be? (and any variation of this)
Stars-7) Which is brighter, a B0V star or a G0I star?
Stars-8) Develop a sequence of steps which a star will go through as it runs out of hydrogen and
leaves the main sequence. Make a separate sequence low mass stars and another for high
mass stars.
Stars-9) What happens to the outer appearance of a star of 1 solar mass when it runs out of
hydrogen in its core?
Stars-10) What happens to the outer appearance of a star of 8 solar masses when it runs out of
hydrogen in its core?
Stars-11) What type of stellar remnant will our Sun leave when it dies?
Stars-12) If you were going to look for a star which will explode, what type of star would you look
for? (What mass? state of evolution?)
Milky Way and other Galaxies (Units 70, 74, 75)
Get an overall idea that a galaxy is a group of stars with their associated gas, dust, magnetic
field. Know how they look, so that you could tell a spiral from a barred spiral from an elliptical in a
picture. Don’t worry about distinguishing the subtle differences of the types of ellipticals etc. Know
where we live in our spiral galaxy.
Understand the Hubble constant and how we deduce the expansion of the Universe from it. Be
able to relate distance to velocity. If there was a problem about this, I would tell you a value for
the Hubble constant, and ask you for either the distance of the body given the speed, or the
speed given the distance.
Get a picture of the number of galaxies in the universe and that they are arranged in clusters and
that the clusters are in filaments (the places where the galaxies are located are arranged like the
rubber in a sponge, or like the soap film in a bubble bath). Understand that galaxies cluster, how
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the clusters may have started, how there are voids and sheets of large numbers of galaxies, how
we are developing maps of the distribution of galaxies.
Gals-1) What is the evidence that there is dark matter inside of galaxies?
Gals-2) What is the evidence that the Universe is expanding?
Gals-3) What is the evidence that galaxies collide with one another? In what way are their shapes
changed by the collisions?
Gals-4) How do we know that galaxies are distinct groupings of stars and mass, rather than all
part of one object?
Gals-5) What are the names of different types of Galaxies?
Gals-6) What is the tuning fork diagram? How does it relate to the evolution of galaxy types?
Gals-7) Are galaxies in the early Universe the same as galaxies today? If not, what are some of
the differences?
Gals-8) What is the strongest evidence that there is something in galaxies in addition to all the
stars, gas and dust we can detect?
Gals-9) What is the Hubble law?
Gals-10) What is the distance of a galaxy whose radial velocity is 3000km/sec?
Gals-11) What is the local group? Approximately how many members does it have
Gals-12) What is a void?
Gals-13) What do we think is the reason that voids occur ?
Gals-14) What is the evidence that there is dark energy?
Cosmology (Units 80, 82)
Get an overall history of
Big Bang
Creation of Some of the Elements
Creation of the galaxies etc
Continuing expansion of the entire thing ( or Big Bounce??)
Be able to outline the history of the Universe
Cosmol-1) What evidence is there that the Universe is expanding?
Cosmol-2) What would, or wouldn’t make it contract again?
Cosmol-3) Why do we think that there is material in the Universe in addition to the stars, gas,
and dust which we can see?
Cosmol-4) Where does the Helium in the universe come from? Where does the Iron come from?
Cosmol-5) How does the amount of deuterium in the Universe help us determine the baryon
density?
Cosmol-6) What is the Cosmic Background Radiation?
Cosmol-7) Why is it surprising that the early universe was very nearly isotropic (the same density
everywhere)?
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