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What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

1. 5GmM/6R
2. 2GmM/3R
3. GmM/2R
4. GmM/2R

Correct answer: 5GmM/6R

Solution

Minimum energy = E_final - E_initial = -GMm/(2*3R) - (-GMm/R) = GMm/R (1 - 1/6) = 5GMm/(6R).

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