Physics 321 -- Spring 2006

Homework #10, due at
beginning of class Wednesday April 12.

1. [8pts]
A spacecraft in elliptical orbit about the earth has a speed of 10km/sec at
its perigee (distance of closest approach) which is 6700km from the center
of the earth.

(a) How far away from the center of the earth is it at apogee (farthest distance)?

(b) How fast will it be moving at the apogee?

(c) How long will it take for it to reach apogee? (This part can be done using
computer aid for the integral, or by using the Kepler formula for the period.)

(d) Find the distance travelled between perigee and apogee.

2. [4pts]
Marion & Thornton, problem 8-14 (same in Edition 4).
Hint: You can start with angular momentum conservation.

3. [4pts] Marion & Thornton, problem 8-23 (same in Edition 4). Hint: Use the effective potential V(r) to
calculate the maximum radial velocity.
Then you’ll need to do some algebraic manipulations to get the answer in
the form given in the book.

4. [4pts] Marion & Thornton, problem 8-24 (same in Edition 4). Hint: don’t forget to add the Earth’s radius
(use 6400km) when you calculate the orbital distances.

5. [4pts]
Marion & Thornton, problem 8-42 (same in Edition 4).
Calculate the energy supplied in each of the two "burns" separately.
Your answers should be in Joules -- rocket scientists are known for mixing up units!