1) If a binary star system is close enough to the Earth, then Astronomers can measure the distance to the system directly via parallax. They can also easily measure the angular size of the system and, by watching the companion star's motion over time, the period. So you may assume that distance, angular size and period are known.

a) (7 pts) How do we deduce the orbital distance of the companion star? Explain.

b) (7 pts) If this system is face-on, state in a single sentence why we cannot use Doppler shift information to deduce the orbital velocity of the companion star, then explain how we find the orbital velocity of the companion.

2) Name and explain two reasons why the overall size of the Sun very slowly increases over the course of its main sequence lifetime.

3) For this question, assume that we are using the inverse square law without the "X" correction for interstellar reddening and extinction.

a) (7 pts) Star A and star B have the same apparent luminosity and the same absolute luminosity, but star A is suffering from interstellar reddening (no extinction). Explain how this affects our estimate of star A's absolute luminosity and our estimate of star A's distance. Will we estimate that star A is closer or further away?

b) (7 pts) Star A and star B have the same absolute luminosity and the same distance from the Earth, but star A is suffering from interstellar extinction (no reddening). Explain how this affects our estimate of star A's apparent luminosity and our estimate of star A's distance. Will we estimate that star A is closer or further away?

4) Explain what a forbidden line is. As part of your answer, explain why forbidden lines are not generally seen in gases with very high densities, like those gases found on Earth.

5) The radioactive isotope Aluminum-26 (Al-26) is a kind of atom that is only formed naturally during supernova explosions, and it decays to a more stable atom within an astronomically short timescale (about a million years).

a) (7 pts) Explain why the presence of Al-26 decay traces in meteorites that have landed on Earth is seen as evidence a supernova caused the initial collapse of the solar nebula into our solar system.

b) (7 pts) Suppose the decay timescale (or half-life) of Al-26 were 10 billion years instead of just 1 million years. Would the Al-26 decay traces still be seen as evidence of a link between supernova and solar system formation? Explain.

6) Stars have a definite mass range of about 0.08 solar masses to 300 solar masses. No object with a mass outside of that range exists stably as a star.

a) (7 pts) Explain why stars have a minimum possible mass.

b) (7 pts) Explain why stars have a maximum possible mass.

7) In a binary system, one star starts with a higher mass than the other. After some time, star A is seen to be a red giant star while star B is seen to be a red main sequence star.

a) (7 pts) Which star probably was more massive to begin with? Explain your answer.

b) (7 pts) After some more time passes, the red giant undergoes a planetary nebula phase, leaving behind a white dwarf with a companion star close enough so that some of the companion's mass is periodically lost to the white dwarf. Explain how this situation leads to the phenomenon of a recurring nova.

8) Although the disk of the Milky Way galaxy generally has a blue color, the stars within the disk have a variety of ages.

a) (7 pts) Explain why the light from the disk of the Milky Way as a whole is blue.

b) (7 pts) Suppose Astronomers were to discover an individual red main sequence star in the disk of the Milky Way. Would they deduce that its age is younger, older or about the same as the Sun? Or can the age even be deduced? Explain your answer.