Motion of Orbiting Satellites Practice Test

A satellite in elliptical orbit obeys Kepler’s second law; what happens to its speed as it approaches perigee?

In circular orbit, gravity supplies the centripetal force: $\frac{GMm}{r^2}=\frac{mv^2}{r}$. This yields $v=\sqrt{\mu/r}$ and, combining with $v=2\pi r/T$, gives Kepler’s 3rd law $T^2\propto r^3$. How does the gravitational force act as the centripetal force for an orbiting satellite?