1) The only direct method Astronomers are able to use for determining the distances to other nearby stars is through the method of parallax. By measuring "parallax angles", astronomers can estimate the distances to these stars.

a) (6 pts) Use a simple diagram and a couple of sentences to explain how parallax angles are related to stellar distances. In other words, if star A is further away than star B, will star A's parallax angle be larger, smaller or the same as star B's parallax angle?

b) (5 pts) Use your answer to part (a) to help explain why astronomers in Kepler's era were unable to observationally verify the heliocentric model of the solar system.

2) The equation for absolute luminosity and the inverse square law are given below:

Star A has the same apparent luminosity and the same size as star B, but star A has a higher surface temperature (12,000 K) than star B (6,000 K). Assuming there is no need for a correction factor due to reddening and/or extinction...

a) (3 pts) Which of these two stars is closer to Earth (A, B, same distance)?

b) (8 pts) Explain your answer to part (a).

3) A Hydrogen atom has an electron in the lowest energy level. There are two possible ways for this atom to absorb light. The first is excitation, a process in which an electron moves up from a lower energy level to a higher energy level. The second is ionization, a process in which the electron escapes the atom.

a) (5 pts) Which of these two processes requires a higher frequency photon? (excitation, ionization, same frequency for both). Explain your answer.

b) (6 pts) Use your answer from (a) to help explain why ionized gases are typically found where temperatures are extremely high.

4) Two stars, Regulus and Rigel, have the same composition and the same surface temperature. Neither star has a significant rotation velocity. When spectra are taken of the two stars, Astronomers notice that the absorption lines in Rigel's spectrum are much narrower than those in Regulus' spectrum. You may assume for this problem that there is no interstellar material (gas or dust) that is found along our line of sight to either star.

a) (3 pts) Rregulus is probably (larger, smaller, the same size) compared to Rigel.

b) (8 pts) Explain your answer to part (a). Just saying something like, "Regulus is ____________ compared to Rigel because it has narrower lines." will result in no credit. You need to explain why line width has anything to do (or nothing to do) with the size of a star.

5) Energy in stars is typically transported from the core to the surface by radiation, convection or a combination of the two.

a) (3 pts) In the region of the Sun's envelope close to the core, energy is transported mainly via (radiation, convection).

b) (8 pts) Explain your answer to part (a).

6) Two gas bulbs are filled with Oxygen gas and then heated so that the gases inside give off emission lines. Bulb A emits a spectrum corresponding to singly-ionized Oxygen (O II). Bulb B emits a spectrum corresponding to triply-ionized Oxygen (O IV).

a) (3 pts) Which bulb has hotter gas inside (A, B, same temperature)?

b) (8 pts) Explain your answer to part (a). As I warn elsewhere in this exam, just saying something like, "A is hotter because it emits O II" will result in no credit. You have to explain why temperature is (or is not) related to the information given.

7) One way Astronomers double-check our theory of how the Sun works is to observe neutrinos that are produced by the Sun's core. The latest experiments have found about 1/3 of the number of neutrinos expected by theorists.

a) (6 pts) Explain why we can use neutrinos to test our theories about the Sun's core. Why not use easier-to-observe visible light instead?

b) (5 pts) Given this contradiction between theory and observation, explain why Astronomers continue to believe that the theory of nuclear fusion in the Sun's core is valid.

8) Stars with the same surface temperature and composition as the Sun tend to show singly ionized Iron lines prominently in their spectra. Stars that have temperatures substantially different than the Sun, even though they may have the same composition as the Sun, will not show singly-ionized Iron lines. Explain why stars with substantially cooler temperatures will not show these lines.

9) The light curves for two eclipsing binaries show that system A's companion star has a period that is twice as long as the period of system B's companion star. The equation of orbital velocity that applies to binary star systems is:

These two systems are close enough that the angular separation between the two stars and the distance from the Earth to each system has been determined.

a) (5 pts) Explain how the distance from Earth and angular separation for a given binary system can be used to find the orbital distance, rorbit, of the companion star from the central star.

b) (6 pts) Assume that the orbital distances for each system have been found to be identical. Which system has a more massive central star? Justify your answer either mathematically or in a couple of sentences.

10) Suppose you're an alien astronomer looking at our own solar system with an edge-on perspective. From your vantage point, your spectral observations show that as the Earth orbits the Sun, the absorption lines seen from Earth's atmosphere will shift from red to blue depending on the Earth's motion. Suppose you decide to point your telescope at Mars, a planet further from the Sun than Earth. Will the spectral lines caused by Mars shift more or less than Earth's spectral lines? Use the equation of orbital velocity (elsewhere in this exam) to help explain your answer.