PHYSICS 321 - Classical Mechanics I

Spring 2007

Homework Set #10 (due 4/18/07)

(but note that this section is on the midterm exam of 4/13!)

1. Thornton and Marion, problem 8-23. Hint: Use the effective potential V(r) to calculate the maximum radial velocity. Then you will need to do some algebraic manipulations to get the answer in the form given in the book.

2. Thornton and Marion, problem 8-24. Don’t forget to add the radius of the Earth when you calculate the orbital distances.

3. Thornton and Marion, problem 8-27. Hint: Use conservation of angular momentum.

4. Thornton and Marion, problem 8-37. This problem is worded strangely. It refers to the calculations of Section 8.8. 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 radius of the Earth to the “height” to get the radius of the orbit.

5. Thornton and Marion, problem 8-42.

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