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Work Done by Force of Gravity

A space vehic...

Question

A space vehicle of mass m is in a circular orbit of radius $2 R_{e}$ about the earth $(m_{e})$ . What is the work done by an external agent to transfer it to an orbit of radius $4 R_{e}$ ?

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Solution

Total energy $T . E = \frac{- G m_{e} m}{2 r}$

Work done $W = T . E_{f} - T . E_{i}$

So, $W = \frac{- G m_{e} m}{8 R_{e}} - (\frac{- G m_{e} m}{4 R_{e}})$

$⟹ W = \frac{G m_{e} m}{8 R_{e}}$

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