Download The scale of the Universe (along with units and scientific notation)

The scale of the Universe (along with units and
scientific notation)
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http://people.physics.tamu.edu/quadri/astr101_fall16/
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Read Chapter 2 for class on Tuesday
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The first assignment is due before class on Tuesday.
Access the homework site (“Pearson Mastering
Astronomy”) through eCampus.
•
First create an account on Mastering Astronomy using
the access code that came with your textbook (a separate
code is available for purchase)
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If you have trouble, see the Pearson representative today
and tomorrow 9am-5pm outside the bookstore entrance,
first floor MSC
If the sun were the size of a grapefruit…
If the sun were the size of a grapefruit…
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the Earth would be the size of the point of a pen 15m
away (that’s 50ft)
If the sun were the size of a grapefruit…
•
the Earth would be the size of the point of a pen 15m
away (that’s 50ft)
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Jupiter would be the size of a marble 80m away
If the sun were the size of a grapefruit…
•
the Earth would be the size of the point of a pen 15m
away (that’s 50ft)
•
Jupiter would be the size of a marble 80m away
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Pluto would be 600m away
If the sun were the size of a grapefruit…
•
the Earth would be the size of the point of a pen 15m
away (that’s 50ft)
•
Jupiter would be the size of a marble 80m away
•
Pluto would be 600m away
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the nearest stars, in the Alpha Centauri system, would
be 2700 miles away
If the sun were the size of a grapefruit…
•
the Earth would be the size of the point of a pen 15m
away (that’s 50ft)
•
Jupiter would be the size of a marble 80m away
•
Pluto would be 600m away
•
the nearest stars, in the Alpha Centauri system, would
be 2700 miles away
Most of space is empty. That’s why we call it “space”!
Most of space is mostly empty. So remember that when
you see images like this
One of the stars in the Alpha Centauri system, Proxima
Centauri, was recently found to have an orbiting planet
that might be at just the right temperature to have liquid
water… which is promising for the possibility of life
One of the stars in the Alpha Centauri system, Proxima
Centauri, was recently found to have an orbiting planet
that might be at just the right temperature to have liquid
water… which is promising for the possibility of life
•
The New Horizons spacecraft, which recently flew by
Pluto, attained an ultimate velocity of 51,000mph. At
this rate it would take ~60,000 years to reach Proxima
Centauri
Breakthrough Starshot
One of the stars in the Alpha Centauri system, Proxima
Centauri, was recently found to have an orbiting planet
that might be at just the right temperature to have liquid
water… which is promising for the possibility of life
•
The New Horizons spacecraft, which recently flew by
Pluto, attained an ultimate velocity of 51,000mph. At
this rate it would take ~60,000 years to reach Proxima
Centauri
•
The new Breakthrough Starshot project, which aims to
launch tiny spacecraft at ~20% the speed of light, may
be able to get there in ~25 years
Our galaxy, the Milky Way, has over 100 billion stars
(that’s 100,000,000,000). How big of a number is that?
Our galaxy, the Milky Way, has over 100 billion stars
(that’s 100,000,000,000). How big of a number is that?
That’s about the number of seconds between 1000B.C.
and now
This image, from the Hubble Space Telescope, is of such a
zoomed-in region of the sky that you could cover it with a
grain of sand held at arm’s length
The number of stars in the observable universe is
comparable to the number of grains of dry sand on all the
beaches on Earth
Not only is the Universe really big, it’s also really
old
Not only is the Universe really big, it’s also really
old
Not only is the Universe really big, it’s also really
old
Scientific notation
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1 astronomical unit (AU) is approximately 90 million
miles, or 90,000,000 miles.
Scientific notation
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1 astronomical unit (AU) is approximately 90 million
miles, or 90,000,000 miles.
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Let’s rewrite this in a more useful notation:
Scientific notation
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1 astronomical unit (AU) is approximately 90 million
miles, or 90,000,000 miles.
•
Let’s rewrite this in a more useful notation:
Scientific notation
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1 astronomical unit (AU) is approximately 90 million
miles, or 90,000,000 miles.
•
Let’s rewrite this in a more useful notation:
Scientific notation — the rules
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First, realize that 10x is just 1 with x zeros behind it
Scientific notation — the rules
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First, realize that 10x is just 1 with x zeros behind it
100 = 1
101 = 10
102 = 100
103 = 1000
Scientific notation — the rules
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First, realize that 10x is just 1 with x zeros behind it
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Next, rewrite any large number such that the decimal is
after the first digit, and multiplied by 10x
Scientific notation — the rules
•
First, realize that 10x is just 1 with x zeros behind it
•
Next, rewrite any large number such that the decimal is
after the first digit, and multiplied by 10x
Scientific notation — the rules
•
First, realize that 10x is just 1 with x zeros behind it
•
Next, rewrite any large number such that the decimal is
after the first digit, and multiplied by 10x
Scientific notation — the rules
•
First, realize that 10x is just 1 with x zeros behind it
•
Next, rewrite any large number such that the decimal is
after the first digit, and multiplied by 10x
— or, to put it another way —
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Move the decimal over to the left until it is after the first
digit. The number of places that you moved it is the
exponent x.
Scientific notation — the rules
•
First, realize that 10x is just 1 with x zeros behind it
•
Next, rewrite any large number such that the decimal is
after the first digit, and multiplied by 10x
— or, to put it another way —
•
Move the decimal over to the left until it is after the first
digit. The number of places that you moved it is the
exponent x.
Scientific notation — but what about tiny numbers?
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It works just the same for tiny numbers, but the
exponent is negative and this time you move the
decimal place to the right
Scientific notation — addition & subtraction
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If the exponents are the same, then just add or subtract
the coefficients:
Scientific notation — addition & subtraction
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If the exponents are the same, then just add or subtract
the coefficients:
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If the coefficients aren’t the same, then first make them
the same… then add or subtract:
Scientific notation — multiplication & division
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Just multiply or divide the coefficients, and add or
subtract the exponents
Significant figures
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This room is 34ft across. How far is that in yards?
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Enter 34/3 into your calculator: the answer is
11.3333333…
Significant figures
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This room is 34ft across. How far is that in yards?
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Enter 34/3 into your calculator: the answer is
11.3333333…
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But how precise do we need to be? Do we really care
about all of those significant figures?
Significant figures
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This room is 34ft across. How far is that in yards?
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Enter 34/3 into your calculator: the answer is
11.3333333…
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But how precise do we need to be? Do we really care
about all of those significant figures?
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And even if we wanted to be super-precise, is it even
correct to print out so many significant figures? What
if the room is actually 34’2” across? Then your
calculator will say 11.388888… yards across, and so
your original answer is wrong!
Significant figures
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Because we do not know precisely how far across this
room is in feet, it is incorrect to quote the length in
yards to a very high degree of precision.
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Your answer should have the same precision as the
input values: in this example you should quote only
two significant figures. This room is 34 feet, or 11 yards,
across.
Significant figures
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The two rules of significant figures:
Significant figures
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The two rules of significant figures:
Your final answer should have the same degree of
precision as the least precise of your input values.
Significant figures
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The two rules of significant figures:
Your final answer should have the same degree of
precision as the least precise of your input values.
When doing calculations that involve several steps, use
more significant figures than necessary. Then round your
final answer to the correct number of significant figures.
This reduces the chance of round-off errors.
Significant figures
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What is 6.7/𝛑? Recall that 𝛑=3.14159….
Significant figures
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What is 6.7/𝛑? Recall that 𝛑=3.14159….
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Your calculator prints 2.132678. So round that to 2.1
Significant figures
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What is 6.7/𝛑? Recall that 𝛑=3.14159….
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Your calculator prints 2.132678. So round that to 2.1
What is 6.700/𝛑?
Significant figures
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What is 6.7/𝛑? Recall that 𝛑=3.14159….
•
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Your calculator prints 2.132678. So round that to 2.1
What is 6.700/𝛑?
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Your calculator print 2.132678. So round that to 2.133
Units
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Whenever giving a measurement, you must also
specify the units. Otherwise the measurement is
meaningless.
Units
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Scientists, engineers, and much of the rest of the world
uses the metric system: “meter-kilogram-second” (mks)
or “centimeter-gram-second” (cgs)
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1 meter = 100 centimeters
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1 kilogram = 1000 grams
Units
•
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Scientists, engineers, and much of the rest of the world
uses the metric system: “meter-kilogram-second” (mks)
or “centimeter-gram-second” (cgs)
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1 meter = 100 centimeters
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1 kilogram = 1000 grams
Compared to the “fps” system:
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1 meter = 3’3” (slightly longer than a yard)
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1 kilogram = 2.2 pounds
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also, 1 kilometer = 0.62 miles
Units
In astronomy, we typically deal with *very* large
numbers, so it is useful to use different types of units
Units
In astronomy, we typically deal with *very* large
numbers, so it is useful to use different types of units
Distance:
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1 astronomical unit (AU) = 1.5x108 km. This is the
average distance from the Sun to the Earth
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1 lightyear = 9.4x1012 km. This is the distance
traveled in one year at the speed of light
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1 parsec = 3.26 lightyears. We will talk about the
definition of a parsec later this semester
Units
In astronomy, we typically deal with *very* large
numbers, so it is useful to use different types of units
Mass:
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1 Earth Mass (M ) = 5.97x1024kg
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1 Solar Mass (M⊙) = 2x1030kg
⨁
Units
Units can be treated like variables
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Addition and subtraction
1s + 2s = 3s
Units
Units can be treated like variables
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Addition and subtraction
1s + 2s = 3s
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Multiplication and division
6m × 6m = 36m2
10s/2s = 5
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
wrong!
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
wrong!
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
wrong!
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
wrong!
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
wrong!
Units
Getting the correct units in a calculation is a useful sanitycheck!
•
How long does it take to drive from College Station
to Houston?
wrong!
incorrect units, so we know that
we have an incorrect answer
Unit conversions
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Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
Unit conversions
•
Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
1ft = 0.305m
Unit conversions
•
Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
1ft = 0.305m
0.305m
1=
1ft
Unit conversions
•
Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
1ft = 0.305m
0.305m
1=
1ft
m
1 = 0.305
ft
Unit conversions
•
Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
1ft = 0.305m
0.305m
1=
1ft
m
1 = 0.305
ft
Unit conversions
•
Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
Unit conversions
•
Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
Unit conversions
•
Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
Unit conversions
•
Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
Unit conversions
•
Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
Unit conversions
•
Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
Unit conversions
•
Mars has an orbit with radius 1.5AU. How far is it from
Earth at closest approach, in miles? Use the fact that
1AU=9.3x107mi
Unit conversions
•
Mars has an orbit with radius 1.5AU. How far is it from
Earth at closest approach, in miles? Use the fact that
1AU=9.3x107mi
1.5AU
1AU
Unit conversions
•
Mars has an orbit with radius 1.5AU. How far is it from
Earth at closest approach, in miles? Use the fact that
1AU=9.3x107mi
0.5AU
1.5AU
1AU
Unit conversions
•
Mars has an orbit with radius 1.5AU. How far is it from
Earth at closest approach, in miles? Use the fact that
1AU=9.3x107mi
Unit conversions
•
Mars has an orbit with radius 1.5AU. How far is it from
Earth at closest approach, in miles? Use the fact that
1AU=9.3x107mi
Unit conversions
•
Mars has an orbit with radius 1.5AU. How far is it from
Earth at closest approach, in miles? Use the fact that
1AU=9.3x107mi
Unit conversions
•
Mars has an orbit with radius 1.5AU. How far is it from
Earth at closest approach, in miles? Use the fact that
1AU=9.3x107mi
Problems
1. How many seconds would it take to travel around the
earth at the speed of light?
•
c=3x108 km/s, Earth radius=6370 km
•
Recall that distance=velocity×time and
circumference=2𝛑r
Problems
1. How many seconds would it take to travel around the
earth at the speed of light?
•
c=3x108 km/s, Earth radius=6370 km
•
Recall that distance=velocity×time and
circumference=2𝛑r
2. How long does it take light to travel from the Sun to
Earth? (give the answer in minutes)
•
1 AU = 1.5x108 km
Problems
1. How many seconds would it take to travel around the
earth at the speed of light?
•
c=3x105 km/s, Earth radius=6370 km
•
Recall that distance=velocity×time and
circumference=2𝛑r
2. How long does it take light to travel from the Sun to
Earth? (give the answer in minutes)
•
1 AU = 1.5x108 km
3. If the Sun were to suddenly just disappear, what would
happen to the Earth? And how long would it take to
happen?
1. How many seconds would it take to travel around the
earth at the speed of light?
•
c=3.0x108 km/s, Earth radius=6370 km
•
Recall that distance=velocity×time and
circumference=2𝛑r
1. How many seconds would it take to travel around the
earth at the speed of light?
•
c=3.0x108 km/s, Earth radius=6370 km
•
Recall that distance=velocity×time and
circumference=2𝛑r
That’s about 1/8 of a second. If you were traveling at the
speed of light, you could go around the Earth 8 times in one
second
2. How long does it take light to travel from the Sun to
Earth? (give the answer in minutes)
•
1 AU = 1.5x108 km
2. How long does it take light to travel from the Sun to
Earth? (give the answer in minutes)
•
1 AU = 1.5x108 km
2. How long does it take light to travel from the Sun to
Earth? (give the answer in minutes)
•
1 AU = 1.5x108 km
3. If the Sun were to suddenly just disappear, what would
happen to the Earth? And how long would it take to
happen?
3. If the Sun were to suddenly just disappear, what would
happen to the Earth? And how long would it take to
happen?
•
It will get very dark (even the moon will be dark)… but
only after about 8 minutes
3. If the Sun were to suddenly just disappear, what would
happen to the Earth? And how long would it take to
happen?
•
It will get very dark (even the moon will be dark)… but
only after about 8 minutes
•
The Earth will fly out of it’s circular orbit… but only after
about 8 minutes. We won’t really feel anything though
3. If the Sun were to suddenly just disappear, what would
happen to the Earth? And how long would it take to
happen?
•
It will get very dark (even the moon will be dark)… but
only after about 8 minutes
•
The Earth will fly out of it’s circular orbit… but only after
about 8 minutes. We won’t really feel anything though
•
It will gradually get colder, and colder, and colder