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A satellite of mass m=1.50e+3 kg is in circular orbit around the Earth, and the radius of this orbit is R =1.11e+4 km. Take the
A satellite of mass m=1.50e+3 kg is in circular orbit around the Earth, and the radius of this orbit is R =1.11e+4 km. Take the mass of the Earth to be ME =610^24 kg. The satellite is subject to a small frictional force of magnitude f=0.0889 N due to the outer atmosphere of the Earth. Because of this force, the satellite will slowly spiral back towards Earth. What is the change in radius r of the satellite after one revolution (assuming the starting radius is r0 as given above)? Hint: Assume that the change in radius is slow enough that at any instant of the orbit the satellite can be considered to be undergoing circular motion. Also, since this change in radius will be small, in the sense that r/r0 1, you may (and should) use a Taylor expansion to find a close (i.e., first-order) approximation to the exact
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