Question

A satellite of mass $1000kg$ is supposed to orbit the earth at a height of $2000km$ above the earth's surface. Find the potential energy of the earth-satellite system.

Answer 1

The potential energy is given by

$U=-\frac{GMm}{r}=-\frac{gm{R}^2}{R+h}$

$U=-\frac{9.8\times 1000\times {(6.4\times 10}^6{)}^2}{6.4\times {10}^6+2\times {10}^6}\approx 4.76\times {10}^{6}J$

Answer is $4.76\times {10}^{6}J$