More Final Exam Review Questions

1. What can you use the Virial Theorem to derive? Go ahead and do the derivations!
2. What is the temperature of a black marble placed in an orbit 2 AU away from the Sun?
3. What is the Jeans Mass and Jeans Radius for a giant molecular cloud, how does they relate to star formation, and how do you derive these quantities? HINT: there are two methods
4. What is the speed of a Jupiter-mass planet in orbit 1 AU from a 1 Msun star? How does this speed relate the the speed of the central star?
5. What is the approximate relationship between the location of the habitable zone around a star and the mass of the star? 
6. What is the transit duration of a Jupiter-size planet around a 1 Msun star? How about for a 2 Msun star?
7. What is the scale height of a planet's atmosphere? How does the scale height of a nitrogen-dominated atmosphere (like ours) compare to that of a pure hydrogen atmosphere?
8. Two stars are in orbit around each other separated by 1 AU. Star A has a mass of 2 Msun while Star B has a mass of 0.5 Msun. What are their relative speeds? What are their relative semimajor axes? What are their orbital periods? If they eclipse, how long does the eclipse last (keep in mind that both stars are moving)?
9. How can we use the Sun's spectrum, along with other observations of the Sun to measure the AU?
10. Two planets orbit a Sun-like star. One planet has a radius of 1 Rjup, and the other has a radius equal to the Earth's. Compare the transit depths.
11. How does the velocity of a star orbited by a planet depend on the mass of the planet, the semimajor axis of the orbit and the mass of the star?
12. How fast is a particle moving in a gas cloud of temperature T?
13. Astronomers often assume that the luminosity of a main-sequence star scales as $L \sim M^4$. Where does this come from?
14. The target field of the NASA Kepler Mission was at an RA of 18 hours and a declination of +30. When does the target field cross the meridian at midnight? Can we observe stars in the Kepler field from Cambridge tonight?
15. What is the flux at the surface of a star of radius $R_\star$ and temperature $T$? How does this flux change at a distance $d > R_\star$?
16. Check out the visual binary star Alberio by doing a Google images search. Compare the properties of the two stars.
17. Why are red dwarf stars such good targets for searching for habitable-zone planets?
18. What is the main sequence? How is luminosity related to effective temperature on the main sequence?
19. If a star is 4 magnitudes brighter than another star, what is the flux ratio of the two stars? Try this question for various values of the magnitude difference.
20. How does the flux of a star depend on its distance? How does its magnitude depend on distance?
21. What are the (approximate) transit parameters of the following transit light curves assuming that all of the planets have 3-day orbits?
    
22. Assuming the central star has a mass of 2 $M_\Sun$, what are the properties of this planet? Compare your properties to that of Pollux b.
    
23. How does the luminosity of a star depend on its temperature and radius?
24. How does the surface flux of a star depend on it's temperature and radius?
25. What is the speed of Jupiter compared to the speed of the Earth? Compare their momenta. Compare their kinetic energies.
26. What is the diffraction limit of the human eye observing at 0.5 micron?
27. What is the diffraction limit of a 100 meter telescope observing at 1mm?
28. What is the angular diameter of the Sun as viewed from Saturn (approximately 9 AU)?
29. What is the angular diameter of the Sun as viewed from alpha Centauri A (approximately 1 pc)?
30. How many AU away is alpha Cen A?
31. If the Sun were powered by gravitational collapse, how long would it shine at its current luminosity?
32. How does the lifetime of a star scale with its mass? Look up the stars in the alpha Cen triple system on Wikipedia. Compare their lifetimes.