Physics 220 Class Exercise October 9 2000
 

We were asked to find the radius of a geosynchronous orbit. We start with the free-body diagram for the satellite:
 
 

geosynchronous orbit

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

Thus:

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

and so

r = 4.2´ 107 m = 6.6 Earth Radii.