UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
2008 FALL STARS Professor Martin
HOMEWORK PROBLEM #1 Due: September 29th
Assigned Reading: Phillips 1.1-1.4, 1.7
Problem 1: Consider a spherically symmetric gas cloud of uniform den-
sity ρ0. We showed that if all pressure support is removed, the cloud will
collapse to a point on the free-fall timescale.
(a, 2 pts) Evaluate the integral R1
0qx
1−xdx in the derivation and verify
that the answer given in class for the free-fall timescale is correct. [See
Chapter 1 of Phillips for hints.]
(b, 1 pts) Now consider a molecular cloud with the following properties:
temperature T= 20 K, mass M= 1000 M¯, and density n= 105hydrogen
molecules per cubic centimeter. If the pressure forces supporting this cloud
were removed, how long would it take the cloud to collapse to a point? [Hint:
Just calculate the free-fall time. You are given more information than you
actually need.]
(c, 2 pts) Find the gravitational potential energy of a uniform, spherical
cloud of total mass Mand radius R. [Hint: Use Eqn. 1.6 to show that the
coefficient in 1.16 is 3/5.]
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