 
Summary: Physics 314 (Survey of Astronomy) Exam 2
Please show all significant steps clearly in all problems.
Please give clear, legible, and reasonably complete (although brief) responses to qualitative questions.
See the last page for values of constants.
1. Black holes
(a) (4) Calculate the escape velocity from the surface of the Earth, which has a radius of 6.37!106
meters
and a mass of 5.98!1024
kg. (The sum of the kinetic energy and gravitational potential energy is the same at
the Earth's surface as at infinity, so you can first algebraically solve for the escape velocity in terms of the
known quantities.)
As in Eq. (7.3) of the textbook,
vesc =
2GM
R
= 1.12 !104
m/s.
(b) (4) Again using nonrelativistic physics and Newtonian gravity, just as in part (a), calculate the
Schwarzschild radius of a black hole with mass M . Comment on the validity of each of these two
approximations for very strong gravitational fields, and on the validity of the final answer.
