If the zero of potential energy is chosen at infinity, what is the relation between the total energy

Question

If the zero of potential energy is chosen at infinity, what is the relation between the total energy ($E$) and the kinetic energy ($K$) of an orbiting satellite?

Professor PC Thomas Classes · Answer

For a satellite in a circular orbit, Potential Energy $U = -\frac{GMm}{r}$ and Kinetic Energy $K = \frac{GMm}{2r}$. The total energy is $E = U + K = -\frac{GMm}{2r}$, which implies $E = -K$. Thus, the total energy is negative and equal in magnitude to the kinetic energy.