The energy needed to raise the satellite to a height 'h' is
Δv=vA−vB
=−GMmR+h−(−GMmR)
=GMmhR(R+h)
=GMmhR2(1+hR)GMR2=g
=mgh(1+hR)=E1
E2= energy of the satellite
=12mv20(v0−orbital velocity )
r- distance of satellite from center of earth
=12m(GMr)
=12m(GMR+h)
=12m(GMR2)R(1+hR)
E2=mgR2(1+hR)
∴E1E2=2hR