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Consider two satellites $A$ and $B$ of equal mass, moving in the same circular orbit of radius $r$ around the earth but in the opposite sense and therefore a collision occurs. Find the total mechanical energy $E_{A} + E_{B}$ of the two satellite-plus-earth system before collision.

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$\frac{G M m}{r^{2}}$

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

$\frac{- G M m}{r^{2}}$

$\frac{G M m}{r}$

answer is B.

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Detailed Solution

$E = 2$ (energy of one satellite)

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

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