Homework #2, due Monday, Oct 8

1. Complete any work remaining on the Class Exercise on the Solar System. Provide your excel spreadsheet and the plot of orbital velocity vs orbital radius. Be sure to answer these questions:
(a) How does the plot compare to equation we derived from the law of gravity and circular motion, v²=GM/r ?
(b) Compare the values you calculate for mass contained with the radius of the different planets and explain your results. (Hint: look at the relative numbers and recognize that you should be rounding the answers to no more than 3 significant figures.)

2. (a) What is meant by mass-to-light ratio?
(b) What is the mass-to-light ratio of the Sun?
(c) The plot on this page shows the "mass-luminosity relation" for stars. The luminosity of a star in this plot is determined by the rate at which it fuses hydrogen to helium. This is strongly mass-dependent. Find the mass-to-light ratio of a star that is 10 times more massive than the sun (look at the x-axis at 10 solar masses, then find the corresponding luminosity and find the mass-to-light ratio). Then find the mass-to-light ratio of a star 0.5 solar masses. (You will need to estimate).
(d) From (c), you can see that the mass-to-light ratio of a collection of stars will depend on what stars make up the collection. We say that a stellar population typically has a mass-to-light ratio of 2-3, based on the most common types of stars. What does that tell you about the mass of the most common type of stars (e.g., about the mass of the sun? More massive than the sun?)

3. Review 21-cm radiation emitted by atomic hydrogen (HI), the summary of parameters we can measure using the HI emission line, and HI distribution in galaxies.
(a) What three parameters can be measured using the HI emission line spectrum? Which parameters are based on the Doppler Effect and what velocities are we measuring?
(b) Why does measuring the velocities of HI gas in galaxies allow us to trace a galaxy's mass to larger radii than just measuring the stellar velocities?