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A satellite is moving around the Earth, whose radius is R, in a circular path of radius 3R. The percentage rise in the energy needed to place it into a circular orbit of radius 5R is

1. 10%
2. 20%
3. 30%
4. 40%

Correct answer: 40%

Solution

Total orbital energy E = -GMm/(2r). Going from 3R to 5R, E rises by GMm/R*(1/6 - 1/10) = GMm/(15R). As a fraction of the initial magnitude GMm/(6R), the increase is (1/15)/(1/6) = 6/15 = 40%.

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