Physics - Gravitation Question with Solution | TestHub

The kinetic energy of a satellite of mass $m$ orbiting a planet of mass $M$ in a circular orbit of radius $r$ is given by $K=\frac{GMm}{2r}$.

The potential energy of the satellite is $U=-\frac{GMm}{r}$.

The total energy of the satellite is the sum of its kinetic and potential energies:

$E=K+U=\frac{GMm}{2r}-\frac{GMm}{r}=-\frac{GMm}{2r}$

Comparing the expressions for total energy and potential energy, we get:

$E=\frac{1}{2}\left(-\frac{GMm}{r}\right)=\frac{U}{2}$

Thus, the total energy of a circularly orbiting satellite is half of its potential energy.

Answer: half the potential energy of the satellite.