# Gravitation/Average Force Problem

1. Nov 26, 2007

### brendan3eb

1. The problem statement, all variables and given/known data
What are (a) the speed and (b) the period of a 220 kg satellite in an approximately circular orbit 640 km above the surface of Earth? Suppose the satellite loses mechanical energy at the average rate of 1.4x10^5 J per orbital revolution. Adopting the reasonable approximation that the satellite's orbit becomes a "circle of slowly diminishing radius," determine the satellite's (c) altitude, (d) speed, and (e) period at the end of its 1500th revolution. (f) What is the magnitude of the average retarding force on the satellite? Is angular momentum around Earth's center conserved for (g) the satellite and (h) the satellite-Earth system?

2. Relevant equations
w=change in mechanical energy
w=FDcos(x)

3. The attempt at a solution
First and foremost, I've solved parts a-e correctly. I just need to get f-h.
(1500 revs)((-1.4x10^5 J)/rev)=-2.1x10^8 J
W=change in mechanical energy
W=-2.1x10^8 J
W=FDcos(x)
FDcos(x)=-2.1x10^8 J
So F is definitely the unknown I have to solve for, therefore I should be able to get D and x. Do I just assume that x is 0 degrees? And for finding D, do I just choose one of the two radius values and multiply the amount of revs by the circumference?

It seems to me as though the above way of solving is a little questionable. The only alternative would be a calc-based solution, but I am not quite sure how to go about that.