Consider a small satellite moving in a circular orbit(radius) about a spherical planet(mass).Which expression gives this satellites orbital velocity?
The gravitational acceleration between the satellite of mass m moving arround a spherical plannet of mass M and radius r is given by:
F = GMm/r^2, but this is also the centrepetal force due to the velocity v of the satellite which is mv^2/r
Therefore, mv^2/r = GMm/r^2 or
v = sqrt(GM/r) = (GM/r) ^(1/2).