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Astronomy Basics
Science and Technology
Science has to do with the discovering of relationships in
nature. Scientists are not concerned with people's opinions
of what they are doing. A scientist searches for physical facts
and truths regardless of whether they are "useful" to the
public or not.
Technology deals with the tools, techniques, and procedures
for making practical use of the facts that science discovers.
Technology emphasizes "people" and is only concerned with
what is practical and useful to people. Technology is very
concerned with the reactions of the public. If people will not
like it - technology stays away from it.
What is Astronomy?
Simply put, it is the study of the material universe that is
above the Earth's atmosphere.
Physics, astronomy, mathematics and even religion were
intertwined early in the development of modern science. The
“father of modem science”, Galileo, was both an astronomer
and physicist.
Astronomy vs. Astrology
Be careful not to confuse astronomy – the natural science
studying the universe above the Earth’s sky – with astrology
- a pseudoscience claiming divination by the positions of the
planets and sun and moon.
While the zodiac is an astronomical term, horoscopes are not
scientific and have no significance in astronomy.
Science and Math
About 400 years ago, it was discovered that much of nature could be described
and analyzed mathematically. When scientific ideas are expressed mathematically,
then the ideas become unambiguous (i.e. very clear). Science became a great
success when mathematics and experimentation were united with it.
The Scientific Method
1.
2.
3.
4.
5.
Recognize a problem.
Make an educated guess - a hypothesis.
Predict the consequences of the hypothesis.
Perform experiments to test the predictions.
Make the simplest general rule that organizes
the hypothesis, prediction, and experimental outcome.
Science is "self-correcting". If the results of the experiments contradict the
hypothesis, then there is a problem and the scientist returns to step 1. In step
2, the previous hypothesis must either be revised or discarded altogether.
Not all great scientific discoveries are made by following the "scientific
method". Sometimes great progress is made in science by trial and error,
experimentation with guessing, or "by accident" (i.e. good luck). Roentgen
discovered X-rays by accident!
Fact: a close agreement by competent observers of a series of observations of
the same phenomena.
Hypothesis: an educated guess; not accepted as factual until successfully
checked out over and over again by experiment by many different
scientists.
Law or Principle: a statement about the relationship between natural quantities
that has been tested over and over again and has not been
contradicted.
Theory: a large body of information that encompasses well-tested and verified
hypotheses about certain aspects of the natural world.
Scientific Notation
When scientists work with very large or very small numbers, they use a system
called scientific notation. This shortens numbers by substituting powers of 10 in
place of long strings of zeros. For example:
Number Decimal
Scientific Notation
45,000,000
4.5 x 107
0.0000000813
8.13 x 10-8
36,000
3.6 x 104
0.000005421
5.421 x 10-6
Can you figure out how to write these numbers below in scientific notation?
Give it a try.
Wavelength of red light is 0.00000065 m.
Wavelength of green light is 0.00000050 m.
The nearest star, Alpha Centauri (Proxima), is
43,000,000,000,000 kilometers (km) away.
The nearest large galaxy, Andromeda, is
2.2 million light-years away, ...or
22,000,000,000,000,000,000 km away.
Venus is 40,000,000 km from the Earth.
The radius of the Earth is 6378 km.
The diameter of the sun is 1,392,000 km.
Length of a white blood cell is 0.00001 cm.
Wavelength of red light is 0.00000065 m.
6.5 10 7 m
Wavelength of green light is 0.00000050 m.
5.0 107 m
The nearest star, Alpha Centauri (Proxima), is
43,000,000,000,000 kilometers (km) away.
4.3 10 13 km
The nearest large galaxy, Andromeda, is
2.2 million light-years away, ...or
22,000,000,000,000,000,000 km away.
2.2 10 19 km
Venus is 40,000,000 km from the Earth.
4 10 7 km
The radius of the Earth is 6378 km.
6.378 10 3 km
The diameter of the sun is 1,392,000 km.
1.392 10 6 km
Length of a white blood cell is 0.00001 cm.
1 105 c m
Constellations
A natural human tendency is to see patterns and relationships between
objects even when no true connection exists, and people long ago
connected the brightest stars into configurations called constellations.
• In the Northern Hemisphere, most constellations were named after
mythological heroes and animals. (e.g. Greek mythology - Orion)
• The stars making up a particular constellation are generally NOT close
together in space. They merely are bright enough to observe with the
naked eye and happen to lie in the same direction in the sky as seen from
Earth.
• Constellations provide a convenient means for astronomers to specify
large areas of the sky, much as geologists use continents
The Constellation
Orion
(a) A photograph of the
group of bright stars
that make up the
constellation Orion.
(Trout)
(b) The stars connected
to show the pattern
visualized by the
Greeks: the outline of a
hunter. You can easily
find this constellation in
the northern winter sky
by identifying the line of
three bright stars in the
hunter’s belt.
(c) The 3-dimensional
relationships for the
prominent stars in
Orion. The Greek
letters are astronomical
notations indicating
brightness.
(S. Westphal)
The Celestial Sphere
Over the course of a night, the constellations appear to move across the
sky from east to west, but the relative positions of stars remain
unchanged. It was natural for the early astronomers to conclude that the
stars were attached to a celestial sphere surrounding Earth—a canopy of
stars like an astronomical painting on a heavenly ceiling.
Figure P.2 The Celestial Sphere
Planet Earth sits fixed at the hub of
the celestial sphere, which contains
all the stars. This is one of the
simplest possible models of the
universe, but it doesn’t agree with the
facts that astronomers now know
about the cosmos.
The apparent motion of the stars is the result of the spin, or rotation, of the Earth.
Even though the celestial sphere is an incorrect description of the heavens, we still
use the idea as a convenient fiction that helps us visualize the positions of stars in
the sky.
The point where Earth’s axis
intersects the celestial sphere in
the Northern Hemisphere is
known as the north celestial
pole; it is directly above Earth’s
North Pole. In the Southern
Hemisphere, the extension of
Earth’s axis in the opposite
direction defines the south
celestial pole.
Midway between the north and
south celestial poles lies the
celestial equator.
The star Polaris, often
called the “North Star”,
indicates the direction—
due north—in which the
axis of Earth’s rotation
points.
Celestial Coordinate System – Method 1
• The simplest method of locating stars in the sky is to specify their
constellation and then rank the stars in it in order of brightness. The
brightest star is denoted by the Greek letter  (alpha), the second brightest
by  (beta), and so on.
• Because there are many more stars in any given constellation than there are
letters in the Greek alphabet, this method is of limited utility. However, for
naked-eye astronomy, where only bright stars are involved, it is quite
satisfactory.
Celestial Coordinate System – Method 2
• If we think of the stars as being
attached to the celestial sphere
centered on Earth, then the familiar
system of latitude and longitude on
Earth’s surface extends quite naturally
to the sky. The celestial analog of
latitude is called declination, and the
analog of longitude is called right
ascension.
• Just as latitude and longitude are tied
to Earth, right ascension and
declination are fixed on the celestial
sphere. So the stars may appear to
move across the sky because of Earth’s
rotation, but their celestial coordinates
remain constant. over the course of a
night.
North Celestial Pole
Right
Ascension
Lines
Earth
Declination
Lines
Celestial Equator
South Celestial Pole
Declination is measured in degrees.
Right ascension is measured in
hours, minutes and seconds.
A Solar Day vs. A Sidereal Day
Solar and Sidereal Days
The Earth revolves around the
Sun at the same time as it
rotates on its axis.
A solar day is the time from
one noon to the next.
0.986
Sun
Earth
Earth’s orbit
One sidereal day later (aligned with stars)
One solar day later (aligned with Sun)
Because Earth completes one
circuit (360°) around the Sun in
one year (365 days), it moves
through 360o /365 days =
0.986o per day. Thus, between
noon at point A on one day and
noon at the same point the
next day, Earth rotates through
almost 361°.
Consequently, the solar day
exceeds the sidereal day (360°
rotation) by about 3.9 minutes.
Short-Term (Daily) Changes
I. The sun rises in the east and sets in the west each day due to the Earth's
rotation. Length of day varies with season.
II. The moon rises in the east and sets in the west each day due to the
Earth's rotation. Moonrise is about 50 minutes later each day.
III. The planets rise in the east and set in the west each day due to the
Earth's rotation. The times will depend on the rate of the planet's motion
with respect to the stars.
IV. The stars rise in the east and set in the west each day due to the
Earth's rotation. At our 40o latitude, some stars never set. They are
called circumpolar stars. A timed-exposure picture of the night sky
shows that the stars appear to rotate about the "north star" (Polaris).
Star rise is about 4 minutes earlier each day.
Seasonal Changes
• In six months Earth moves to the opposite side of its orbit, and
we face an entirely different group of stars and constellations
at night. Because of this motion, the Sun appears, to an observer
on Earth, to move relative to the background stars over the course
of a year. This apparent motion of the Sun on the sky traces out
a path on the celestial sphere known as the ecliptic.
• The 12 constellations
through which the Sun
passes as it moves along
the ecliptic — that is, the
constellations we would
see looking in the direction
of the Sun if they weren’t
overwhelmed by the Sun’s
light — are collectively
known as the zodiac.
North Celestial Pole
The ecliptic lays
in the plane of
Earth’s orbit
around the Sun.
Earth
23 ½ o
Celestial Equator
South Celestial Pole
Autumnal
Equinox
Winter
Solstice
Sun
Summer
Solstice
Vernal Equinox
Plane of the Ecliptic
autumnal
equinox
winter
solstice
Sun
aphelion
perihelion
summer
solstice
vernal
equinox
The Earth’s orbital plane
as seen from above the
north pole. The orbit’s
ellipticity has been greatly
exaggerated for clarity.
The Solstices
• The point on the ecliptic where the Sun is at its northernmost point above
the celestial equator is known as the summer solstice. This occurs on or
near June 21—the exact date varies slightly from year to year because the
actual length of a year is not a whole number of days. On that date,
points north of the equator spend the greatest fraction of their time in
sunlight, so the summer solstice corresponds to the longest day of the
year in Earth’s Northern Hemisphere and the shortest day in Earth’s
Southern Hemisphere.
• Six months later the Sun is at its southernmost point below the celestial
equator. We have reached the winter solstice (December 21), the
shortest day in Earth’s Northern Hemisphere and the longest in the
Southern Hemisphere.
The Equinoxes
• The two points where the ecliptic intersects the celestial equator are
known as equinoxes. On those dates, day and night are of equal
duration. (The word equinox derives from the Latin for “equal night.”)
In the fall (in Earth’s northern hemisphere), we have the autumnal
equinox (on September 21). The vernal equinox occurs in spring, on or
near March 21, as the Sun crosses the celestial equator moving north.
• The vernal equinox plays an important role in human timekeeping. The
interval of time from one vernal equinox to the next—365.242 solar
days—is known as one tropical year.
Long-Term Changes
• The time required for Earth to complete exactly one orbit around the Sun,
relative to the stars, is called a sidereal year. One sidereal year is 365.256
solar days long, about 20 minutes longer than a tropical year. The reason for
this slight difference is a phenomenon known as precession. Like a spinning
top that rotates rapidly on its own axis while that axis slowly revolves about
the vertical, Earth’s axis changes its direction over the course of time.
• Earth’s precession is caused by the combined gravitational pulls of the
Moon and the Sun and a complete cycle of precession takes about 26,000
years.
• Because of this slow shift in the orientation of Earth’s rotation axis, the
vernal equinox drifts slowly around the ecliptic over the course of the
precession cycle. So the seasons slowly shift - eventually January will be
a summer month and Orion will be a summer constellation!
• This precession also causes the pole star to change over time. For
example, in the year 14,000 AD, Vega will be our pole star.
Measuring the Night Sky
One distance-measurement method is
called triangulation. It is based on the
principles of Euclidean geometry and
finds widespread application today in
both terrestrial and astronomical settings.
Knowing two angles in a triangle and the
length of the side shared by the angles
(called the baseline in the diagram), then
the lengths of the other two sides of the
triangle can be determined.
The apparent displacement of a
foreground object relative to the
background as the observer’s
location changes is known as
parallax.
The closer an object is to the
observer, the larger the parallax.
The amount of parallax is
inversely proportional to an
object’s distance. Small parallax
implies large distance. Conversely,
large parallax implies small
distance. So parallax is a
powerful method for measuring
astronomical distances.
When an object is nearby, it spans a greater arclength than when it is far away.
The ball has an angular diameter of when it is close by, and an angular
diameter of , which is smaller, when it is far away. The angular diameter
of an object will depend on its distance.
Simple Measuring Instruments
The unit used to measure angles in astronomy is the degree. There are 3600
in a circle. Each degree is divided into sixty equal parts called minutes (or
arcminutes). Each minute is divided into sixty equal parts called seconds
(or arcseconds). So we have:
1 arcminute = 1/60th degree
1 arcsecond = 1/60th minute = 1/3600th degree
Sextant
A sextant provides two coordinates for position of object in sky: often
elevation (or altitude) which is the angle above the horizon, and azimuth
which is the angular position along the horizon, measured clockwise from
north.
C
mirror 1
A
mirror 2
eyepiece
B
moveable
arm
vernier
O
The Human Hand
While not terribly accurate, can be used to estimate angles in the sky.
Horizon and Zenith
The horizon is the imaginary line where the sky and earth meet if there were no
terrain in the way - ocean level at the shore is the horizon.
The zenith is the point directly overhead (altitude angle = 900).
Measuring the Size of the Earth, Moon and Sun
Eratosthenes, a Greek mathematician and geographer, measured the
circumference of the Earth (235 B.C.) to within 5% of our modern day
estimate.
Aristarchus measures the moon's diameter and distance from the Earth by
watching eclipses of the moon (240 B.C.) He was also within 5% of the
modern day accepted values.
Aristarchus measured the sun's diameter and distance from the Earth by
taking angular measurements when the moon was half full. (His results were
not as successful here because of his crude measurements and perhaps his
bias. He determined the sun to be 20 times more distant than the moon, when
in fact it is really 400 times more distant.)
Gerver's Method
for Measuring the Earth's Diameter at the Ocean Shore
Apparatus: a pointed rock on a hill, a line of string, a meterstick
Procedure:
1. Find a hill that gives you a clear view of the ocean horizon in opposite
directions (a peninsula) with a pointed rock at the top. Ideally the hill should
be between 100 and 1000 feet above sea level.
2. Mount the meterstick upright about 15 ft. from the pointed rock. Measure this
distance exactly. This is b.
3. Stand on the other side of the meterstick from the rock and adjust your
eyelevel until the pointed rock lines up with the ocean horizon. Note where
your line of sight intersects the ruler. (The string may be helpful for this.)
4. Now move to the other side of the rock and repeat step 3. The distance
between the two points of intersection on the meterstick is a.
5. Your height above sea level is h. If you don't know your height above sea
level, then you will have to come up with some clever means of determining
it. Perhaps you can devise a geometry trick similar to this method in order to
calculate it.
6. Calculate the radius of the Earth as approximately 8hb2 /a2 . Because of light
refraction in the atmosphere, your sighting of the horizon will be in slight
error. This refractive effect makes Gerver's computed radius too large by
about 20%. So the radius of the Earth will be closer to
But if a<<b, then the radius of the Earth can be approximated as:
Rawlins' Method
for Measuring the Earth's Diameter at the Ocean Shore
CAUTION: This procedure requires you to "watch" a sunset. Even at sunset looking
directly into the sun for any length of time can harm your eyes. The greatest danger is
from the ultraviolet radiation which is invisible to your eye and can cause damage to
your eye before you feel any pain. Keep track of the sun's motion by looking off to the
side of it, or by giving it an occasional quick glance. It is best to not gaze until the sun
is mostly below the horizon. You may wish to consider purchasing "eclipse glasses"
from a scientific company or getting an appropriate welding shield from a welding
supply store.
Apparatus: stopwatch, meterstick
Procedure: (NOTE: Use standard S.I. Units…meters for distances and seconds for time.)
1. Find a place where you have a clear view of the sunset* on a beach or one of
the Great Lakes. The water should be calm the day you perform your
measurements. Approximate the height of the waves on the ocean in meters.
This amount is ho, It will probably be about 0.6 meters or so.
2. Observe the first sunset while sitting on the beach. (Laying down to observe is
possible, but only if the body of water is particularly calm.) Measure the height
of your eyes above sea level. This amount is h1.
3. As soon as the last visible part of the sun ducks below the horizon, start your
stopwatch and run quickly up the steps on the boardwalk to a higher elevation.
(Simply jumping to your feet raises you eyelevel some - perhaps enough if you
are very accurate with the stopwatch.)
* This procedure is for sunset. Appropriately revising the procedure should work for
sunrise.
4. Being at a higher elevation, you will see the sun set AGAIN! Stop the
stopwatch as soon as you see the last visible part of the sun duck below the
horizon. The time on your stopwatch is t. The height of your eyes above sea
level at this new observing position is h2
5. A couple of corrective factors must be made since the speed at which the sun
sets will depend on your latitude and what time of year it is. To account for
these, find the values for A and B in the charts below that correspond to your
latitude and date (or as close to it as you can approximate). There is also an
error due to the refraction of light
caused by the Earth's atmosphere.
This will be approximately accounted
for in the equation below, so you don't
have to worry about it.
6. Calculate the radius of the
Earth as: