Physics 321 -- Spring 2004

Homework #10, due at beginning of class Wednesday April 14.

1.         [6pts] 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.)

2.         [4pts] Marion & Thornton: problem 8-17.

3.         [4pts] 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.         [4pts] Marion & Thornton, problem 8-24.  Don’t forget to add the Earth’s radius (you can use 6400km) when you calculate the orbital distances!

5.         [4pts] Marion & Thornton, problem 8-42.  Your answer should be in Joules.

6.         [4pts] Marion & Thornton, problem 8-37. This problem is worded strangely. You should 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.         [4pts] Marion & Thornton, problem 8-14. Hint: You can start with angular momentum conservation.