Gravitaional potential energy

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Question

A satellite is moving around the earth (Radius = R) in a circular orbit of radius 2R with kinetic energy K. The satellite is suddenly stopped and then released. What will be the kinetic energy of the satellite just before it strikes the surface of earth?

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Solution

$K = \frac{GMm}{2 (2 R)} = \frac{GMm}{4 R}$
Conserving energy, $K' + (\frac{- GMm}{R}) = - \frac{GMm}{2 R}$
$\Rightarrow K' = \frac{GMm}{R} - \frac{GMm}{2 R} = \frac{GMm}{2 R} = 2 K$

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