Gravitation/Average Force Problem

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The discussion focuses on calculating the speed, period, altitude, and average retarding force of a satellite in a circular orbit around Earth, considering energy loss per revolution. The user has successfully solved parts a-e and seeks guidance on parts f-h, particularly in determining the average retarding force and the conservation of angular momentum. They express uncertainty about assuming the angle in the work equation and how to calculate distance based on the satellite's radius. The conversation emphasizes the need for clarity on the appropriate equations and methods to approach the remaining parts of the problem. Overall, the user is looking for assistance in refining their calculations and understanding the physics involved.
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Homework Statement


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?


Homework Equations


w=change in mechanical energy
w=FDcos(x)

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.
 
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I'm not asking for a solution, but some help as to what equations and steps I should take to solve this problem. Thanks.
 

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