1. Astronomy 1 – Fall 2014
CLM - Fall 2014
Lecture 4; October

2. Previously on Astro-1
Planets appear to move on the sky mostly West to East but occasionally with “retrograde motions”
The ancients thought that the Earth was at the center of the solar system and that planets moved in spheres around the Earth
epicycles explained retrograde motion
In the modern Heliocentric model, the planets go around the sun (copernican model)
What pieces of evidence show that the Geocentric model is false?
Kepler’s Laws
The orbits of planets are ellipses
A planet’s speed varies along the orbit
The period of the orbit is related to the size of the orbit
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3. Previously on Astro-1 Newton’s Laws of Motion: Inertia
Relation between force and acceleration
Action/Reaction
Inertial and gravitational mass
Newton’s Law of gravity
The orbits of planets
Tides
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4. Today on Astro-1 The nature of light.
Properties of light emitted by opaque sources.
Spectral lines
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5. Is the speed of light finite? Galileo tried, but couldn’t measure it.
In 1676 Olaus Rømer noticed that the measurements of the eclipses of Jupiter’s moons were systematically off, depending on how distant Earth was from Jupiter. From this he deduced the speed of light (in terms of AU).
Figure 5-1 Rømer’s Proof That Light Does Not Travel Instantaneously
Thetiming of eclipses of Jupiter’s moons as seen from Earth depends on the
Earth-Jupiter distance. Rømer correctly attributed this effect to variations
in the time required for light to travel from Jupiter to the Earth.
CLM - Fall 2014

6. Properties of Waves Example: Interference

7. Young’s Double-Slit Experiment Illustrates that Light is a Wave
Figure 5-5 Young’s Double-Slit Experiment
(a) Thomas Young’s classic double-slit
experiment can easily be repeated in the modern laboratory by shining
light from a laser onto two closely spaced parallel slits. Alternating dark
and bright bands appear on a screen beyond the slits.
CLM - Fall 2014

8. Light is Electromagnetic Radiation
But what “wiggles” to make the wave? In 1860 James Clerk Maxwell showed that all forms of light consist of oscillating electric and magnetic fields that move through space at a speed of 3.00 × 105 km/s or 3.00 × 108 m/s. This figure shows a “snapshot” of these fields at one instant.
Figure 5-6 Electromagnetic Radiation
All forms of light consist of
oscillating electric and magnetic fields that move through
space at a speed of km/s m/s. This
figure shows a “snapshot” of these fields at one instant. The
distance between two successive crests, called the
wavelength of the light, is usually designated by the Greek
letter (lambda).
CLM - Fall 2014

9. Frequency and Wavelength of an Electromagnetic Wave
ν = frequency of an electromagnetic wave (in Hz –
a Hertz is one cycle per second)
c = speed of light, 3×108 m/s
λ = wavelength of the wave (in meters)
Example: What is the frequency of visible light at 540 nm?
CLM - Fall 2014

10. Color of Light Depends on Its Wavelength

11. Newton used this experiment to prove that prisms do not add color to light but merely bend different colors through different angles. It also proved that white light, such as sunlight, is actually a combination of all the colors that appear in its spectrum.
4 Newton’s Experiment on the Nature of Light
In a crucial experiment, Newton took sunlight that had passed through a prism and sent it
through a second prism. Between the two prisms was a screen with a
hole in it that allowed only one color of the spectrum to pass through.
This same color emerged from the second prism. Newton’s experiment
proved that prisms do not add color to light but merely bend different
colors through different angles. It also proved that white light, such as
sunlight, is actually a combination of all the colors that appear in its
spectrum.

12. What about “invisible light
What about “invisible light?” Around 1800 British astronomer William Herschel passed sunlight through a prism and held a thermometer just past the red end of the visible spectrum. The thermometer registered a temperature increase, indicating there was “infrared” light that we could not see.
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13. Why is the Sky Blue? CLM - Fall 2014 Box 5-4 Light Scattering
a) Why the sky looks blue
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14. Why is the Sunset Red? CLM - Fall 2014 Box 5-4 Light Scattering
(b) Why the setting Sun looks red
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15. Human Eye is Sensitive to a Small Part of the Electromagnetic Spectrum

16. …but you are familiar with ‘invisible light’
It’s only invisible to the human eye.

17. The Doppler Shift: The Wavelength of Light is Affected by the Relative Motion between the Source and the Observer

18. Doppler Shift Equation
Dl / l = v / c
Dl = wavelength shift
l = wavelength if source not moving
v = speed of the source along the line of sight
c = speed of light = 3e5 km/s

19. Demo: Doppler Shift of Sound Waves (iclicker Question)
A speaker is whirled around on a rope.
The sound from the speaker will do the following.
Rise to higher frequency as the speaker moves towards the listener. Fall to lower frequency as the speaker moves away from the listener.
Fall to lower frequency as the speaker moves towards the listener. Rise to higher frequency as the speaker moves away from the listener.
Get louder as the speaker approaches the listener and get softer as the speaker moves away.
Get louder as the speaker moves away and get softer as the speaker moves towards the listener.
Both A & C

20. Why did the moon turn orange-red during the lunar eclipse
Why did the moon turn orange-red during the lunar eclipse? (iclicker Question)
The moon emits orange-red light because of its temperature.
Red light was scattered towards the moon by the earth’s atmosphere.
The earth emits red light, and we saw that light reflecting off the moon.
The light emitted by the moon was red because of the moon’s Doppler shift.
Sunlight passing through earth’s atmosphere was illuminating the moon. The blue light had been removed by scattering.
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21. The Light Emitted by Opaque Sources “ Blackbody Radiation”
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22. An opaque object emits electromagnetic radiation according to its temperature

23. Temperature is a measure of the average speed of the atoms in an object.

24. Temperature Units
Box 5-1 Temperatures and Temperature Scales
Astronomers use the Kelvin temperature scale. The “degrees” are the same as the Celsius system, only with 273 added, and they aren’t called degrees (just K). The are no negative numbers – “absolute” zero is the coldest possible temperature.
CLM - Fall 2014

25. Hotter Objects Emit More Light
Each curve shows the intensity of light at every wavelength that is emitted by a blackbody at a particular temperature. The rainbow-colored band shows the range of visible wavelengths. The vertical scale has been compressed so that all three curves can be seen; the peak intensity for the 12,000 K curve is actually about 1000 times greater than the peak intensity for the 3000 K curve.
Figure Blackbody Curves
Each of these curves shows the intensity of
light at every wavelength that is emitted by a blackbody (an
idealized case of a dense object) at a particular temperature. The
rainbow-colored band shows the range of visible wavelengths. The
vertical scale has been compressed so that all three curves can be seen;
the peak intensity for the 12,000-K curve is actually about 1000 times
greater than the peak intensity for the 3000-K curve.
CLM - Fall 2014

26. The Hotter the Object the Bluer Its Light
Wien’s Law for a blackbody
λmax = wavelength of maximum emission of the object (in meters)
T = temperature of the object (in Kelvins).
(The K and m above are units of Kelvins and meters).
Figure Blackbody Curves
Each of these curves shows the intensity of
light at every wavelength that is emitted by a blackbody (an
idealized case of a dense object) at a particular temperature. The
rainbow-colored band shows the range of visible wavelengths. The
vertical scale has been compressed so that all three curves can be seen;
the peak intensity for the 12,000-K curve is actually about 1000 times
greater than the peak intensity for the 3000-K curve.

27. Definition of a blackbody
A blackbody is an idealized object that absorbs all radiation falling on it. It does not reflect light, instead it re-emits light.
The temperature of the radiation it emits is determined by the average speed of the atoms in the object.
A blackbody does not have to look black! The Sun is nearly a blackbody.
Most things in everyday life (people, furniture, etc.) are too cool to emit visible light, so you can’t see them in the dark.
Figure Blackbody Curves
Each of these curves shows the intensity of
light at every wavelength that is emitted by a blackbody (an
idealized case of a dense object) at a particular temperature. The
rainbow-colored band shows the range of visible wavelengths. The
vertical scale has been compressed so that all three curves can be seen;
the peak intensity for the 12,000-K curve is actually about 1000 times
greater than the peak intensity for the 3000-K curve.
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28. Cosmic Microwave Background. The CMB is a “perfect” Blackbody
COBE FIRAS 1989; T=2.725 K
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29. Demo: Spectrum of an Incandescent Light Bulb
Passing electrical current through the wire in a lightbulb causes the wire to heat up. How will the light change as the current is increased?
The light will remain white but get brighter.
It will become brighter and bluer.
It will become fainter and bluer.
It will become brighter and redder.
It will become fainter and redder.
CLM - Fall 2014

30. Seeing in the Dark (iclicker Question)
Suppose you want to build a camera that can see people in the dark. Approximately what wavelength does your camera need to be able to image?
X-Rays
Ultraviolet Light
Optical Light
Infrared Light
Radio signals
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31. An Infrared Portrait Human temperature in K = 273+37 = 310K
This is in the infrared!
In this image made with a camera sensitive to infrared radiation, the different colors represent regions of different temperature. Red areas (like the man’s face) are the warmest and emit the most infrared light, while blue-green areas (including the man’s hands and hair) are at the lowest temperatures and emit the least radiation.
Figure 5-10 An Infrared Portrait
In this image made with a camera sensitive to
infrared radiation, the different colors represent regions of different
temperature. Red areas (like the man’s face) are the warmest and emit
the most infrared light, while blue-green areas (including the man’s hands
and hair) are at the lowest temperatures and emit the least radiation. (Dr.
Arthur Tucker/Photo Researchers)
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32. Energy Flux Energy is usually measured in Joules (J).
One joule per second is a Watt (W) – a measure of power.
Flux is the amount of energy passing through one square meter every second.

33. Stefan-Boltzmann Law F = σT4
The Stefan-Boltzmann Law gives the flux of a blackbody of a given temperature.
F = σT4
T = Temperature in Kelvins
The value of the Stefan-Boltmann constant
σ (a constant)= 5.67×10-8 W m-2 K-4.
Figure Blackbody Curves
Each of these curves shows the intensity of
light at every wavelength that is emitted by a blackbody (an
idealized case of a dense object) at a particular temperature. The
rainbow-colored band shows the range of visible wavelengths. The
vertical scale has been compressed so that all three curves can be seen;
the peak intensity for the 12,000-K curve is actually about 1000 times
greater than the peak intensity for the 3000-K curve.
CLM - Fall 2014

34. Energy, Energy Flux & Power Let’s Check that You’ve Got It
In the movie The Matrix – people are used as batteries. If the average human’s bodily surface area is 1.7 m2, and has an average temperature of 37°C, how much energy per second (power) does a person radiate?
Answer. Treating a person as a blackbody, use the Stefan-Boltzmann law to determine the energy radiated per second per square meter, then multiply by the body’s surface area to get the energy radiated per second.
Figure Blackbody Curves
Each of these curves shows the intensity of
light at every wavelength that is emitted by a blackbody (an
idealized case of a dense object) at a particular temperature. The
rainbow-colored band shows the range of visible wavelengths. The
vertical scale has been compressed so that all three curves can be seen;
the peak intensity for the 12,000-K curve is actually about 1000 times
greater than the peak intensity for the 3000-K curve.
Human temperature in K = = 310K
F = σT4 = (5.67×10-8 W m-2 K-4)(310 K)4 = 524 W m-2
Power = 524 W m-2 (1.7m2) = 891 W
About the power of a toaster!
CLM - Fall 2014

35. Power Radiated by Stars (iclicker Question)
Why is a red giant much brighter than a red dwarf?
Red giants are hotter than red dwarfs.
The Stefan-Boltzmann Law tells us that the surface of a red giant emits more energy flux.
The Stefan-Boltzmann Law tells us that the surfaces of all red stars emit the same energy flux.
Red giants are bigger than red dwarfs, so they have more surface area.
Both C & D.
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36. Spectra are the “fingerprints” of atoms and molecules.
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37. Stellar Spectra Have Spectral Lines
Figure 5-12 The Sun as a Blackbody
This graph shows that the intensity of sunlight
over a wide range of wavelengths (solid curve) is a remarkably close
match to the intensity of radiation coming from a blackbody at a
temperature of 5800 K (dashed curve). The measurements of the Sun’s
intensity were made above the Earth’s atmosphere (which absorbs and
scatters certain wavelengths of sunlight). It’s not surprising that the
range of visible wavelengths includes the peak of the Sun’s spectrum; the
human eye evolved to take advantage of the most plentiful light available.
CLM - Fall 2014

38. The Sun’s Spectrum
In 1814 Joseph von Fraunhofer magnified the solar spectrum seen through a prism, and found hundreds of dark lines.
Figure The Sun’s Spectrum
Numerous dark spectral lines are seen in this
image of the Sun’s spectrum. The spectrum is spread out so much that it
had to be cut into segments to fit on this page. (N. A. Sharp,
NOAO/NSO/Kitt Peak FTS/AURA/NSF)
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39. What causes spectral lines?
The structure of atoms
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40. Rutherford’s Experiment
Figure 5-19 Rutherford’s Experiment
Alpha particles from a radioactive source are
directed at a thin metal foil. This experiment provided the first evidence
that the nuclei of atoms are relatively massive and compact.
Rutherford’s Experiment
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41. Rutherford’s model of the atom.
Today we know this is not exactly correct – electrons do not orbit the nucleus, but the basic idea is right -- protons and neutrons exist in the nucleus, and electrons are outside of it.
Figure Rutherford’s Model of the Atom
Electrons orbit the atom’s nucleus,
which contains most of the atom’s mass. The nucleus contains two types
of particles, protons and neutrons.
CLM - Fall 2014

42. “Light is also a Particle”
Planck’s Law
“Light is also a Particle” or
E = Energy of a photon
h = Planck’s constant = 6.625×10-34 J s
c = speed of light
λ = wavelength of light
ν = frequency of light
Figure Blackbody Curves
Each of these curves shows the intensity of
light at every wavelength that is emitted by a blackbody (an
idealized case of a dense object) at a particular temperature. The
rainbow-colored band shows the range of visible wavelengths. The
vertical scale has been compressed so that all three curves can be seen;
the peak intensity for the 12,000-K curve is actually about 1000 times
greater than the peak intensity for the 3000-K curve.
CLM - Fall 2014

43. What is the Energy of a Photon?
Example: DNA molecules are easily broken when hit with ultraviolet light at 260 nm. How much energy does a single photon at this wavelength have?
7.6 x J
7.6 x J
7.6 J
5.7 x J
7.6 x 1019 J
Figure Blackbody Curves
Each of these curves shows the intensity of
light at every wavelength that is emitted by a blackbody (an
idealized case of a dense object) at a particular temperature. The
rainbow-colored band shows the range of visible wavelengths. The
vertical scale has been compressed so that all three curves can be seen;
the peak intensity for the 12,000-K curve is actually about 1000 times
greater than the peak intensity for the 3000-K curve.
CLM - Fall 2014

44. The Bohr model of the atom Niels Bohr 1885-1962
Was a postdoc with Rutherford. In 1912, to explain discrete nature of spectral lines, hypothesized that electron orbits are quantized (quantum mechanics!).
Bohr and Einstein, 1925
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45. The quantum nature of light is related to the quantum nature of atoms!
Figure 5-23
The Absorption and Emission of an H
Photon This schematic diagram, drawn
according to the Bohr model, shows what happens when a
hydrogen atom (a) absorbs or (b) emits a photon whose
wavelength is nm.
(a) Atom absorbs a nm photon; absorbed energy causes
electron to jump from the n = 2 orbit up the n = 3 orbit
(b) Electron falls from the n = 3 orbit to the n = 2 orbit; energy lost
by atom goes into emitting a nm photon
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46. We still call these Balmer lines.
In 1885 Swiss schoolteacher Johann Jakob Balmer, by trial and error, created a formula that can predict where lines of hydrogen fall in the spectrum of a star.
We still call these Balmer lines.
Figure 5-21 Balmer Lines in the Spectrum of a Star
This portion of the spectrum of the star Vega in the constellation Lyra (the Harp) shows eight Balmer
lines, from H at nm through H (H-theta) at nm. The series
converges at nm, slightly to the left of H. (NOAO)
R = Rydberg constant = 1.097×107 m-1
n = any integer greater than 2
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47. The Balmer series and fomula.
R = Rydberg constant = 1.097×107 m-1
Bohr figured out the physical explanation for Balmer’s formula – the spectra from stars depends on the structure of atoms!
Figure The Bohr Model of the Hydrogen Atom
In this model, an electron
circles the hydrogen nucleus (a proton) only in allowed orbits n 1, 2, 3,
and so forth. The first four Bohr orbits are shown here. This figure is not
drawn to scale; in the Bohr model, the n 2, 3, and 4 orbits are
respectively 4, 9, and 16 times larger than the n 1 orbit.
N = lower orbital
n = higher orbital

48. Electron Transitions in the Hydrogen Atom
The same wavelength occurs whether a photon is emitted or absorbed.
Figure 5-24 Electron Transitions in the Hydrogen Atom
This diagram shows the photon
wavelengths associated with different electron
transitions in hydrogen. In each case, the same
wavelength occurs whether a photon is emitted (when
the electron drops from a high orbit to a low one) or
absorbed (when the electron jumps from a low orbit to a
high one). The orbits are not shown to scale.
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49. CLM - Fall 2014 Figure 5-25 Energy-Level Diagram of Hydrogen
A convenient way to display the
structure of the hydrogen atom is in a diagram like this, which shows the
allowed energy levels. The diagram shows a number of possible electron
jumps, or transitions, between energy levels. An upward transition occurs
when the atom absorbs a photon; a downward transition occurs when the
atom emits a photon. (Compare with Figure 5-24.)
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50. Every Element Has a Unique Set of Spectral Lines
Box 5-5 Atoms, the Periodic Table, and Isotopes
The number of protons in an atom’s nucleus is the atomic
number for that particular element. The chemical elements are
most conveniently listed in the form of a periodic table (shown
in the figure). Elements are arranged in the periodic table in
order of increasing atomic number. With only a few exceptions,
this sequence also corresponds to increasing average
mass of the atoms of the elements. Thus, hydrogen (symbol
H), with atomic number 1, is the lightest element. Iron (symbol
Fe) has atomic number 26 and is a relatively heavy
element.
All the elements listed in a single vertical column of the
periodic table have similar chemical properties. For example,
the elements in the far right column are all gases under the
conditions of temperature and pressure found at the Earth’s
surface, and they are all very reluctant to react chemically with
other elements.
Atomic number is the number of protons in an atom.
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51. CLM - Fall 2014 Figure 5-15 Various Spectra
These photographs show the spectra
of different types of gases as measured in a laboratory
on Earth. Each type of gas has a unique spectrum that is
the same wherever in the universe the gas is found.
Water vapor (H2O) is a compound whose molecules are
made up of hydrogen and oxygen atoms; the hydrogen
molecule (H2) is made up of two hydrogen atoms. (Ted
Kinsman/Science Photo Library)
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52. The Ring Nebula is a shell of glowing gases surrounding a dying star.
Nitrogen & Sulpher
Hydrogen & Oxygen

53. Spectroscopy Reveals the Chemical Composition of Celestial Objects
Figure 5-17 Iron in the Sun
The upper part of this figure is a portion of the Sun’s
spectrum at violet wavelengths, showing numerous dark absorption lines.
The lower part of the figure is a corresponding portion of the emission
line spectrum of vaporized iron. The iron lines coincide with some of the
solar lines, which proves that there is some iron (albeit a relatively small
amount) in the Sun’s atmosphere. (Carnegie Observatories)
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54. Kirchoff’s Laws
1. A hot, dense object such as a blackbody emits a continuous spectrum covering all wavelengths.
2. A hot, transparent gas produces a spectrum that contains bright (emission) lines.
3. A cool, transparent gas in front of a light source that itself has a continuous spectrum produces dark (absorption) lines in the continuous spectrum.
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55. Figure 5-16 Continuous, Absorption Line, and Emission Line Spectra
A hot, opaque body (like a blackbody) emits a continuous spectrum of
light (spectrum a). If this light is passed through a cloud
of a cooler gas, the cloud absorbs light of certain
specific wavelengths, and the spectrum of light that
passes directly through the cloud has dark absorption
lines (spectrum b). The cloud does not retain all the
light energy that it absorbs but radiates it outward in
all directions. The spectrum of this reradiated light
contains bright emission lines (spectrum c) with exactly
the same wavelengths as the dark absorption lines in
spectrum b. The specific wavelengths observed depend
on the chemical composition of the cloud.
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56. CLM - Fall 2014

57. CLM - Fall 2014 Figure 5-14 The Kirchhoff-Bunsen Experiment
In the mid-1850s, Gustav Kirchhoff
and Robert Bunsen discovered that when a chemical substance is heated
and vaporized, the spectrum of the emitted light exhibits a series of
bright spectral lines. They also found that each chemical element
produces its own characteristic pattern of spectral lines. (In an actual
laboratory experiment, lenses would be needed to focus the image of the
slit onto the screen.)
CLM - Fall 2014

58. Spectral Lines (iclicker Question)
Professor Martin used a spectrograph on the Keck telescope to observe a distant galaxy. She detected 2 absorption lines from sodium atoms. The wavelengths she measured were 0.22 nm bluer than the wavelengths of and nm where she expected to find the lines. What should she conclude?
There are cool clouds between the observer and the galaxy.
There gas between the galaxy and the observer is hotter than the galaxy.
The gas clouds are moving away from the galaxy towards the observer.
The gas clouds are falling into the galaxy.
Both A and C

59. Structure of Atoms Most of the mass of ordinary matter resides in the
A) electrons and nuclei, shared equally
B) nuclei of atoms
C) electrons around the nuclei of atoms
D) energy stored within the atom in electromagnetic forces
E) Atoms have no mass.
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60. Summary
What is light?
Light is electromagnetic radiation
An opaque object emits light according to its temperture.
Wien’s law: max (in meters) = ( Km)/T.
The Stefan-Boltzmann law: F = T4.
What are photons?
light can have particle-light properties. Particle energy: E = h = hc/
Kirchoff’s Laws
A hot body produces a continuous spectrum
A hot transparent gas produces emission lines
Cool transparent gas in front of a hot body produces absorption lines
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61. Summary Why is the sky is blue and sunsets red?
Blue light is more strongly scattered by the atmosphere than red light
What are stars and interstellar gas made of?
Mostly Hydrogen, He, Oxygen, Carbon
What causes spectral lines?
Atomic structure
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62. Homework – Due 10/20/14
On your own: answer all the review questions in chapter 5
To TAs: answer questions,
5.34 (Note that Io’s surface temperature is -150o C and not 2150o C),
5.37, 5.43, 5.44
CLM - Fall 2014