A satellite of mass m moves in a circular orbit of radius 2R around the Earth (R = Earth's radius). How much additional energy must be supplied to raise it into a circular orbit of radius 4R?

mgR/8
mgR/4
mgR/2
None of these

Correct answer: mgR/8

Solution

For a circular orbit the total energy is E = -GMm/(2r). The energy to move from radius 2R to 4R is the difference of these energies, simplified using GM = gR².

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