What are (a) the speed and (b) the period of a 190 kg satellite in an approximat

Question

What are (a) the speed and (b) the period of a 190 kg satellite in an approximately circular orbit 680 km above the surface of Earth? (a) the speed

(b) the period
Suppose the satellite losses mechanical energy at the average rate of 2.15×104 J per orbital revolution. Adopting the reasonable approximation that the trajectory is a "circle of slowly diminishing radius, " determine the satellite's (c) altitude, (d) speed, and (e) period at the end of its 1500th revolution. (c) altitude( km)
(d) speed

(e) period

(f) What is the magnitude of the average retarding force? (Use the value for the first orbit, enter as a positive number)

Explanation / Answer

a) mv^2/r=GMm/r^2. so v=sqrt(GM/r)=7500(m/s). T=7080e3*2pi/7500=5930(s). b) total energy. mv^2/2-GMm/r=-GMm/2r=-5.345e9(J). after 1500 rounds. A=-5.345e9-1500*2.15e4=-5.377e9. so that r'=7038(km) so altitude h=638(km). --- speed. v=sqrt(GM/r)=7523(m/s) so period T=5880(s). f) average force. F=2.15e4/2pir=4.8e-4(N)

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