The minimum work that has to be performed to bring a spaceship of mass m=2.0×103kg from the surface of the Earth to the Moon is 1.38×10n J where n is:
Potential energy at surface of earth =Ue=−GMemRe
And, g=GMR2
⟹Ue=−mgeRe where ge=g at surface of earth
⟹Ue=−2×103×9.8×6.4×106=−1.4×1011J
At moon, =Um=−GMmmRm=−6.67×10−11×7.35×1022×2×1031.76×106=−5.6×109J
Work done=W=Um−Ue≈1.4×1011J
Hence, n=11