## Problem Set 3

1. [2 pts] Briefly describe the capabilities of each of the instruments on the Spitzer telescope. What does each instrument do that the others do not?

2. [2 pts] (a) From the class handout on extrasolar planets, create a histogram of the frequency of the eccentricities of the 56 objects on the first page. Divide the eccentricities into bins of 0.1, that is, the first bin has objects with 0< e< 0.1, the next bin 0.1< e< 0.2, and so on. Make a separate histogram for the objects on the second page, and a third histogram for the 9 planets in our Solar System listed in Appendix 1.
(b) Compare and constrast these three histograms.

3. [2 pts] Determine a relationship between the masses of stars and their luminosities by plotting log (L/L_sun) vs. log(M/M_sun) for the nearest stars (data compiled in Appendix 4). Hints - Convert the absolute visual magnitude Mv to a luminosity using the Mv of the Sun, which is 4.86. Remember that smaller magnitudes are brighter. Draw a line through the points and measure the slope of the line, and use the slope to get an equation that relates L to M. Write out explicitly how you calculated the luminosity of the first star in the list, Proxima Centauri. Leave all luminosities in units of L_sun, and all masses in units of M_sun.

4. [1 pt] 20-28 of KF (spectrum of reflection nebula)

5. [1 pt] 21-35 of KF (systems with life)

6. [1 pt] 21-31 of KF (mass of H Sun converts to He)

7. [1 pt] 22-34 of KF (age of Ring Nebula)