Introduction to Astrophysics II, 29:120
Spring, 2009
Eighth Homework Set...March 27, 2009. Due April 2, 2009

(1) Derive equation 19.9 in the textbook from equation 19.7.

(2) A solar type star is on an orbit that brings it close to a $10^9 M_{\odot}$ black hole. Calculate the distance at which the star would be tidally disrupted. You will have to make a slight adaptation to the ``classic'' expression for this distance. You should also apply a correction to your estimate by multiplying the distance by a factor of $\frac{2.456}{2^{1/3}}=1.95$. Compare this distance with solar system dimensions.

(3) Assuming that the tidal strain is proportional to the tidal stress, calculate the relative magnitude of Spring Tides and Neap Tides.

(4) To answer this question, you will have to find information on Mars and its atmosphere. Most of the required data will be in your textbook. Calculate the pressure scale height for the atmosphere of Mars, assuming it to be made entirely of carbon dioxide (a good approximation). With this number, calculate an approximate number for the total number of $CO_2$ molecules in the atmosphere of Mars.

(5) Calculate the outgassing speed $\nu$ for Mars.

(6) Use your results for #5 to calculate the outgassing rate $\dot{N}$ for Mars. For this calculation, make the unrealistic assumption that the exosphere occurs at an altitude of 5 scale heights, and that the temperature in the exosphere is the same as at the surface of Mars.

(7) Use the results of #4 and #6 to calculate the atmospheric pressure at the surface of Mars 4 Gyr ago. How does this estimated pressure compare with the surface atmospheric pressure on Earth?

(8) As a result of tidal dissipation, the Earth's rotation will eventually be synchronized with the revolution of the Moon. What will be the length of the day at that time? Simplify the problem by assuming that all of the orbital angular momentum of the Earth-Moon system is in the Moon, and approximate the orbit of the Moon as a circular orbit with a center at the center of the Earth.

(9) Problem 19.18 from the textbook