Physics 321 -- Spring 2003

Homework #10, due Wednesday April 9

1. (2) Marion & Thornton: problem 8-27. Hint: This takes only two lines if you think about it the right way.

2. (3) Marion & Thornton: problem 8-17. Hint: Use conservation of angular momentum and your knowledge of elliptical orbits.

3. (4) Marion & Thornton, problem 8-23. 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. (4) Marion & Thornton, problem 8-24. Don’t forget to add the Earth’s radius when you calculate the orbital distances!

5. (3) Marion & Thornton, problem 8-42. Your answer should be in Joules.

6. (4) Marion & Thornton, problem 8-37. This problem is worded strangely. First find the velocity change for the first “kick” that sends the satellite into an elliptical orbit. Then find the second velocity change needed to convert the orbit back into a circular orbit at the new distance from the Earth. Again, don’t forget to add the Earth’s radius to the “height” to get the radius of the orbit.

7. (5) Marion & Thornton, problem 8-14. Hint: From the equation given for the trajectory, you can calculate dr/dq. Then use the chain rule to derive an expression for dr/dq in terms of dr/dt and the angular momentum l. From that expression you can calculate the potential U(r), and from there you can calculate F(r).