What are the signs of the changes in the kinetic energy ($\Delta K$) and potential energy ($\Delta V

Question

What are the signs of the changes in the kinetic energy ($\Delta K$) and potential energy ($\Delta V$) when a satellite transfers from an orbit of radius $2R_E$ to $4R_E$?

Professor PC Thomas Classes · Answer

Kinetic energy $K = \frac{GMm}{2r}$. As orbital radius $r$ increases from $2R_E$ to $4R_E$, $K$ decreases, so $\Delta K < 0$. Potential energy $V = -\frac{GMm}{r}$. As $r$ increases, $V$ becomes less negative (increases), so $\Delta V > 0$.