The gravitational force 'F' on satellite of mass 'm' revolving around the planet in the orbit of radius 'R' is
F=−GMmR2
Where
G is gravitational constant
M is Mass of the planet.
The work done in increasing the radius of orbit of the satellite through 'dr' is
W=Fdr
but work done is equal to change in gravitational potential '−dV'
therefore
−dV=Fdr
V=−∫3RRFdr
V=−GMmR2∫3RR−(Fdr)
V=GMm∫3RR1R2dr
V=GMmR−GMm3R
V=2GMm3R
Thus work done to increase the radius of orbit of satellite is 2GMm3R