ok, so here's me being desperate. I've covered 4 sheets of paper in useless calculations on this stupid problem, and so, I am giving up. On the small chance that maybe somebody around here will look at this and go, "oh I know how to do that" (*glances at Golly and Grondy...you two know physics at somewhat, right?*) I'm going to post the problem. Any ideas are helpful...I'm totally out at this point. Grondy, you can delete this whole bit after tomorrow if you want, ok?
here's the monster:
A satellite of mass m is in an elliptical orbit around the earth, which has a mass Me and a radius Me. The orbit varies from closest apporach of a at point A to maximum distance of b from the center of the Earth at point B . At point A, the speed of the satellite is Vo. Assume that the gravitational potential energy Ug = 0 when masses are an infinite distance apart. Express your answers in terms of a, b, m, Me, Re, Vo, and G. As the satellite passes point A, a rocket engine on the satellite is fired so that its orbit is changed to a circular orbit of radius a about the center of the Earth. Determine the work done by the rocket engine to effect this change.
blah...have fun...I'm pretty sure there's a simple way to do this, I'm just not seeing it.