The energy required to take a body from the surface of the earth to a height equal to the radius of the earth ( W ). The gravitational potential energy, W‌=‌
GMm
R
−‌
GMm
2R
W‌=‌
GMm
2R
‌‌...‌ (i) ‌ To take body from the surface of the earth to a height to twice of the radius, the energy required ( W′ ) is W′‌=‌
GMm
R
−‌
GMm
3R
‌=‌
2GMm
3R
‌‌...‌ (ii) ‌ Comparing Eq. (i) and Eq. (ii) W′=‌
4
3
W So, the energy required to take the body from the surface of the earth to twice of the radius of the earth is 4∕3W times the energy required.
