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Potential Energy of an Object at a Height

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Question

Find the total mechanical energy $E_{A} + E_{B}$ of the two satellite-plus-earth system before collision.

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Solution

Since total mechanical energy of satellite in radius r is

$E = - \frac{G M m}{2 r}$

Thus,

$E_{A} + E_{B} = 2 (- \frac{G M m}{2 r}) = \frac{G M m}{r}$

Answer is $- \frac{G M m}{r}$

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