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:

*F _{g}* =

*r*^{3} = *GM(T/2p )*^{2}

= (6.7´ 10^{-11} m^{3}/kg·
s^{2})(6.0´ 10^{24} kg)(24
h ´ 3600 s/h)^{2}/(2p
)^{2}

= 7.6´ 10^{22} m^{3}

and so

*r = *4.2´ 10^{7} m =
6.6 Earth Radii.