Question

An artificial satellite moves in a circular orbit around the earth. Total energy of the satellite is given by E. The potential energy of the satellite is

Easy

Solution

We know that, the potential energy of the satellite,
$U = - \frac{G M_{e} m}{R_{e}}$
The kinetic energy of the satellite, $K = \frac{1}{2} \frac{G M_{e} m}{R_{e}}$
The total energy, $E = U + K = - \frac{G M_{e} m}{R_{e}} + \frac{1}{2} \frac{G M_{e} m}{R_{e}} = - \frac{1}{2} \frac{G M_{e} m}{R_{e}}$
$\Rightarrow 2 E = - \frac{G M_{e} m}{R_{e}} \Rightarrow - 2 E = U$
So, potential energy = 2 (total energy)
$\Rightarrow PE = 2 E$

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