PY 124: Solar System Astronomy: Homework 2: SOLUTIONS

1) Explain the process by which an emission spectrum arises. Your explanation should include at least the following terms (used correctly!): Photon, electron, energy level.

An emission spectrum arises when an electrons in an atom fall from a higher energy level to a lower energy level, emitting the difference in energy between the two energy levels as a photon. Each element has a unique set of possible energy levels, so it follows that each element has a unique set of energy level differences and thus a unique set of photon energies that can be emitted. Since the energy of a photon is related to its wavelength and frequency, each element will have a set of wavelengths at which it can emit light. This set is not continuos, but consists only of those few possible wavelengths that correspond to the possible energy differences within the atom. Thus the spectrum of light emitted will be a series of different color lines.

Note that an emission spectrum can only arise in a hot diffuse gas.

2) If the temperature of an object doubles, what happens to the peak wavelength of the emitted light? (If it changes, HOW MUCH does it change?)

Wein's law relates the peak wavelength (lmax) to the temperature (T). lmax T = constant. The temperature is inversely proportional to the peak wavelength. This means that if the temperature doubles, the peak wavelength is cut in half, since if one goes up by a factor of two the other must come down by a fact of two.

3) What attributes do the Jovian planets have in common?

They all have rings. They are all very massive. They all are mainly giant gas balls, and so they have a low density.

4) Why does Venus have a runaway greenhouse effect?

There is a great deal of carbon dioxide (CO2) in the atmosphere of Venus which traps heat in the atmosphere.

5) Compare the age of the Earth, the age of the Solar system, and the age of the Universe.

The age of the Earth and the age of the solar system are believed to be about the same (about 5 billion years), while the age of the universe is at least twice, and perhaps as much as 4 times older (10 to 20 billion years).

6) Describe a method by which you could determine the actual diameter of the planet Mars. You may make any observations you wish from the surface of the Earth. (No satellite data.) Hint: You'll need Kepler's laws.

You would measure the time it takes Mars to orbit the sun. Using this information and Kepler's laws you can determine the distance from the sun to Mars. We know the distance of the Earth to the sun, so we can determine the distance from the Earth to Mars when Mars is as close as it gets to the Earth (at opposition). We then measure the angular diameter of the planet(what angle the planet looks to cover as viewed from the Earth). Knowing the distance and the angular diameter, we can use trigonometry to determine the actual diameter.

7) What attributes do the terrestrial planets have in common?

Higher density than the Jovian planets (about 3 to 5 g/cc). Lower mass than the Jovian planets. Smaller than the Jovian planets. All have a solid surface.

8) List the planets in order out from the sun. Include each planet's mean orbital distance and the time it takes to complete one orbit.

Mercury (0.4 AU, 88 days), Venus (0.7 AU, 225d), Earth (1 AU, 1 Year),

Mars (1.5 AU, 1.8Y), Jupiter (5 AU, 12Y), Saturn (10 AU, 29Y),

Uranus (20 AU, 84Y), Neptune (30 AU, 165Y)

9) What evidence do we have that Mars once had a denser atmosphere?

The dry river beds are an indication that there was once liquid water on the planet. Since the atmosphere is too diffuse at present for liquid water to exist, we believe that the planet must have had a denser atmosphere whenever it had liquid water.

10) List the Terrestrial Planets in order of decreasing atmospheric pressure.

Venus (90 atm.), Earth (1 atm.), Mars (0.1 atm.), Mercury (< 10^-9 atm.)

11) What is the point in a planet's orbit when it is closest to the sun called? What is the point in a planet's orbit when it is farthest from the sun? About when do these occur for the Earth?

Closest: Perihelion (for Earth occurs about January 4)

Farthest: Aphelion (for Earth occurs about July 3)

12) Why can't we just keep adding more lenses to a refracting telescope to remove all of the chromatic aberration?

Because each time the light passes from one lens into another some of the light is reflected away. Thus as we add lenses to reduce chromatic aberration, we lose more of the light. Eventually we completely correct for chromatic aberration, but don't get any light through the telescope!

13) Draw a diagram of the following: A refracting telescope, a Newtonian telescope, and a Cassegrain telescope.

14) What are the advantages of space-based telescopes like the Hubble?

The atmosphere of the Earth does not let all wavelength's through, but above Earth's atmosphere the telescope can see the entire electromagnetic spectrum. Also the Earth's atmosphere causes distortions in the images, which are eliminated in space because there is no atmosphere.

15) Why would we expect that as a general rule more massive planets or moons would have more of an atmosphere?

Essentially because larger planets or moons have higher gravity, so they can hold onto more of the gasses.

Answers to Sample Test 2 on the Web:

1-A, 2-E, 3-A, 4-C, 5-B, 6-B, 7-B, 8-A, 9-B, 10-A, 11-B, 12-C, 13-D, 14-D, 15-C, 16-A, 17-D, 18-D, 19-A, 20-D, 21-C, 22-A, 23-B, 24-D, 25-D

(Updated 12 October 2006 to reflect changes in the sample test)