PowerPoint Presentation Astronomy 112

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Astronomy 112
Dr. Steve Desch Arizona State University Spring
2009
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• RecapWe have discussed the scientific method
• Imagine an explanation for what you see going on.
  
• Make quantitative predictions about what you'll
  observe under particular circumstances.
• Go out and observe, experiment .
• If the experiment matches your prediction... come
  up with new predictions and new experiments.
• If you didn't predict what you actually
  observed... revise your theory.

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• Recap
• We have applied the scientific method to the
  structure of the Solar System
• Kepler's model (building on earlier attempts) is
  the only one consistent with all the
  observations.
• Moon goes around the Earth, Earth/Moon orbit the
  Sun.
• The way the planets orbit obey Kepler's three
  laws
• 1. Planets orbit the Sun in ellipses, with the
  Sun at one focus.
• 2. Period of a planet around the Sun, P, is
  related to semi-major axis of the orbit, a
• P2 a3
• P period in years, a orbit size in AU
• 3. A planet's speed varies along its orbit such
  that it sweeps out equal areas in equal times.

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Recap We have applied the scientific method to
the structure of the Solar System
The order of the planets, the sizes of their
orbits (in AU), and periods of their orbits (in
years) are as follows
Planet a (AU) a3/2 P (yr) Mercury
0.38 0.24 0.24 Venus 0.72
0.61 0.61 Earth 1.00 1.00
1.00 Mars 1.52 1.88 1.88
Jupiter 5.2 11.8 11.8 Saturn
9.6 29.5 29.5
This gives us all the distances once we figure
out what 1 AU is.
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Recap Newton applied the scientific method to
Kepler's laws to explain why planets orbit the
way they do
Newton's laws of motion 1. Objects at rest stay
at rest 2. Objects in motion continue to move in
a straight line at constant speed... unless a
force acts on them. 3. Any time something pushes
on object A, object A pushes back, with an equal
and opposite force.
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Recap Newton applied the scientific method to
Kepler's laws to explain why planets orbit the
way they do
Newton's law of gravity If there are two
objects, one with mass M, the other with mass m,
their mutual gravity pulls them together.
Gravity pulls M toward m, and pulls m toward
M. The magnitude of the force is F G M m /
r2 Where G is a constant and r is the distance
between the masses. This plus vector calculus
predicts elliptical orbits!
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• RecapWe also discussed how we measure 1 AU.
• Stellar aberration is when the Earth's motion
  affects the direction we perceive light to be
  coming from.

Telescope must be tilted to get light to hit the
back of it. The amount of tilt depends on the
Earth's speed and therefore the size of the
Earth's orbit. V/c 0.0001 1 AU (8.3 minutes)
x (speed of light)
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• RecapWe also discussed how we measure 1 AU.
• Eclipses of Jupiter's moons were used by Roemer
  to determine the size of the Solar System.

eclipses on time
eclipses 8 minutes early
eclipses 8 minutes late
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Transits of Venus are the key. Simon Newcomb
used them to determine 1 AU.
Captain Cook 1769
From South Pacific
From England
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Recap Earth's radius 6380 km (Eratosthenes's
experiment) Distance to Moon 385,000 km
(parallax of Moon) Radius of Moon 1750 km (from
its apparent size) Distance to Sun 1 AU
149,000,000 km Radius of Sun 696,000 km Radius
of Jupiter 72,000 km Distance to Saturn about
1,500,000,000 km
1.5 x 109 km
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• RecapHow far away are the stars? And what are
  they?
• Brahe did not find any stars that exhibited
  parallax. He thought it meant the Earth doesn't
  move but that's not consistent with other
  measurements.
• His accuracy was 1 arcminute, so stars must be
  very far away. Simple math (to be discussed
  soon) shows stars must be at least
  500,000,000,000 km away.
• To be seen from so far away, stars must be
  bright...

Earth, December
nearby star
Earth, June
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New Scientific Hypothesis Stars are Suns / The
Sun is a Star.
Are stars other Suns? Is the Sun a star? Guess
who was asking these questions Anaxagoras (c.
450 BC) Aristarchus (c. 220 BC) Giordano Bruno
(1590 AD)
Bruno, in particular, hypothesized that stars
were other Suns, each with their own solar
systems. The idea of aliens with their own
religions was so blaspemous, Bruno was burned at
the stake for daring to suggest it.
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Let us be braver than this and let us dare to
ask. Hypothesis The stars are similar to the
Sun the Sun is a star. Prediction The stars
appear dim to us because they are far away, but
if we could correct for their distance, they
would be as luminous as the Sun. Experiment Use
parallax to measure the distances to the stars,
and then correct for distance. Results ...
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Distance
We can tell how far away a star is by measuring
its parallax.
Earth in December
Earth in June
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Your eyes are separated by only centimeters, but
they have noticeably different perspectives on
nearby objects!
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The distances to nearby stars are measured using
parallax. Parallax is the maximum deviation of
a star from its average position, measured in
arcseconds.
Star B is twice as far away as Star A, so it only
seems to shift half as much
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A parsec is the distance at which a star has a
parallax of 1 arcsecond.
1 parsec (pc) 3.08 ? 1016 m 3.26 light
years (ly) 206,265 AU
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1 arcsecond 1" 1 / 60 of an arcminute 1
arcminute 1' 1 / 60 of a degree 1" 1 / 3600
of a degree 1 / 206,265 of a radian. A nickel
has an apparent width of 1" if it is seen from a
distance of about 1 mile. You try to do this! 1"
is how far apart the eyes of a hiker on Camelback
mountain appear to us. These observations are
impossible without telescopes. But even a
telescope has limits.
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Telescopes tend to concentrate light as if it
were a bunch of rays... the concentrating of
light lets us see dim objects.
eyepiece / camera
mirrors
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On big scales, light travels along rays,
straight lines from the light source to you.
But on small scales (microns 10-6 m), light
fails to travel in straight lines, and smears out
in all directions.
Photographs of stars, if you look closely enough,
look like this
Airy disk First noted by George Airy (1801 -
1892)
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Light smears out when passing through a hole,
just like ocean waves smear out when they pass
through jetties.
Light behaves a lot like ocean waves.
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A wave has a wavelength ?, the distance between
crests. (What are the crests of a light wave?
This will take until the late 1800s to figure
out.)
Light waves have wavelengths!!
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The light of two nearby stars separated by only a
very small angle will be smeared together
(unresolved).
?
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The closest two stars can be in the sky and still
be resolved by your telescope is ?min 0.25 (?
/ ?m) (D / 1 m)
? wavelength of the light D diameter of
telescope
1 1 arcsecond 1 / 3600 degrees 1 ?m 1
micron 10-6 meters
4000 km
NYC
5 m
ASU
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The first parallax of a star was measured by
Friedrich Bessel (1784 - 1846), in 1838 61
Cygni had a parallax of only 0.314
arcseconds! This required a telescope about 1 m
across! 61 Cygni is therefore 1 / 0.314 3
parsecs away The largest parallax of any star is
Proxima Centauri only about 0.7 arcseconds!
Proxima Centauri is therefore 1 / 0.7 1.4
parsecs away Since 1 parsec 1 pc 3.08 x 1016
m, Proxima Centauri 4.2 x 1016 m 4.2 x 1013
km 900,000 AU
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Note Parallax can only be used to measure stars
that are fairly nearby. The observational
uncertainty in the best measurements of the
parallax of a star is about ? 0.001 arcsecond.
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Parallaxes and distances have been measured for
nearest stars There are about 54 stars in 37
systems within 15 light-years 4.6 pc of
Earth. Notice only a few are easy to see.
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Hipparchos introduced a brightness scale called
"magnitudes". The brightest stars were stars of
the "1st magnitude". Almost as bright were stars
of the "2nd magnitude", etc. By modern
definition, stars of 1st magnitude are 100 times
brighter than stars of 6th magnitude. A
difference of 5 magnitudes a factor of 100 in
brightness. (Logarithmic scale) Stars with
large magnitude are faint. Stars with small
magnitude are bright. Stars with negative
magnitude are really bright.
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Sirius -1.4
Canopus -0.7 Alpha Centauri, Arcturus 0.0
Spica, Regulus 1
Polaris, Mizar 2 Megrez 3 Alcor
4 dimmest stars 5 dimmest stars seen in
desert 6
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Sun -27
Sun is 25 magnitudes brighter than Jupiter 5
sets of 5 magnitudes 100 x 100 x 100 x 100 x
100 (102)5 1010 times brighter
Full Moon -12
Venus -4
Jupiter -2
Sirius -1.4 / Canopus -0.7 Alpha
Centauri, Arcturus 0.0 Spica, Regulus 1
Mars 2 / -2
Mercury 0 / -1
Saturn 1
Polaris, Mizar 2 Megrez 3 Alcor
4 dimmest stars 5 dimmest stars seen in
desert 6
Uranus 6
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Luminosity How much light the star puts out
every second, in total. We have to figure this
out. Brightness How bright the star appears to
us or, how much light we receive from the star.
We can measure this.
The brightness of a star depends on its
luminosity and its distance. Luminous stars can
appear dim if they are far. Stars that aren't
luminous can appear bright if they are close by.
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Suppose there are two stars. Star A is 4 times
as bright as Star B. Star A is also 5 times as
far away as Star B.
Which star is more luminous?
How many times as luminous as Star B is Star A?
The luminosity of Star A is 100 times the
luminosity of Star B.
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Example
The star Antares has a parallax of 0.0054
0.0054 arcseconds /- 0.0017 arcseconds. Its
distance is 1 / 0.0054 185 parsecs. 185 parsecs
185 x (3.08 x 1016 m) 5.7 x 1018 m 5.7 x 1018
m ? (1.49 x 1011 m) 3.8 x 107 AU Antares is 38
million times farther away from Earth than the
Sun. If we placed the Sun 3.8 x 107 times farther
away, it would appear (3.8 x 107)2 1.5 x
1015 times dimmer. In fact, the Sun is only 1.6 x
1011 times brighter than Antares. Lantares / Lsun
(bantares / bsun) x (Dantares / Dsun)2
(1 / 1.6 x 1011) x (3.8 x 107)2 9000 Antares
is 9000 times more luminous than the Sun
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Most stars are less luminous than the Sun, but
some stars are far, far more luminous than the
Sun.
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Let us be braver than this and let us dare to
ask. Hypothesis The stars are similar to the
Sun the Sun is a star. Prediction The stars
appear dim to us because they are far away, but
if we could correct for their distance, they
would be as luminous as the Sun. Experiment Use
parallax to measure the distances to the stars,
and then correct for distance. Results ...The
luminosities of stars vary over a range, but the
Sun is in the middle of that range.
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Hypothesis The stars are similar to the Sun
the Sun is a star. Prediction Stars and the Sun
should be made of the same stuff Experiment Use
spectra to determine the composition of the
Sun. Results ...
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SunlightNewton showed that what we perceive as
white sunlight is really many different colors of
light.
..
Not just a Pink Floyd album cover
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These colors are not being created by the prism
they were always there.
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The colors of the rainbow are the colors of
sunlight. Combined, they make white light.
ROY G. BIV
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As any Phoenix resident knows, light is a form of
energy that can heat things up when absorbed.
But thermometers can be heated by "light" with
colors below red, that we cant even see!
We call colors of light "below" red infrared
(IR). There are colors of light beyond violet,
too! ultraviolet (UV). Different colors of
light have different wavelengths!
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This smearing of the light in a telescope, which
depends on the wavelength, is one way we can find
the wavelengths of light waves.
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The interference of light waves with themselves
in a thin film of oil is another way we can
determine the wavelength of light
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Light (electromagnetic radiation) can have any
wavelength! Visible light has wavelengths ?
0.4 - 0.7 ?m. Longer ? infrared, microwave,
radio waves. Shorter ? ultraviolet, X rays,
gamma rays.
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Different wavelengths of light / radiation get
absorbed differently by Earths
atmosphere. Visible light (0.4 - 0.7 microns) and
radio waves (a few cm - 10 m) get through. X-rays
(1 nm), UV (0.1 microns), IR (10 - 100 microns),
millimeter (1 - 10 mm) waves do not.
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Gases do not absorb or emit all possible
wavelengths. They emit only certain wavelengths.
The wavelengths absorbed / emitted by a gas are
unique to that gas!
class demo!
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Gases do not absorb or emit all possible
wavelengths. They emit only certain wavelengths.
The wavelengths absorbed / emitted by a gas are
unique to that gas! We can tell what gas is
there by what colors it emits. It turns out that
gases absorb exactly the same wavelengths of
light that they emit. We can tell what gas
there is by looking at which colors are missing
from a background light source.
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Hydrogen
Oh Be A Fine Girl/Guy Kiss Me
Solar Spectrum
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Spectra of other stars
Notice the absorption lines!
Sun's spectrum
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All stars are mostly made of hydrogen and helium,
with trace amounts of other elements.
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Hypothesis The stars are similar to the Sun
the Sun is a star. Prediction Stars and the Sun
should be made of the same stuff Experiment Use
spectra to determine the composition of the
Sun. Results ...The Sun is made primarily of
hydrogen, with some helium, and trace amounts of
other gases (oxygen, carbon, nitrogen, neon,
etc.). So are other stars, with minor
variations.
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