We were asked to find the radius of a geosynchronous orbit. We start
with the free-body diagram for the satellite:
The force is the gravitational force exerted on the satellite by the Earth. The acceleration is the centripetal acceleration of the satellite. Applying Newton's second law, we have:
Fg = GMm/r2 = mw 2r
r3 = GM(T/2p )2
= (6.7´ 10-11 m3/kg· s2)(6.0´ 1024 kg)(24 h ´ 3600 s/h)2/(2p )2
= 7.6´ 1022 m3
r = 4.2´ 107 m = 6.6 Earth Radii.