## Essential University Physics: Volume 1 (3rd Edition)

We know that their velocity is equal to $v=\frac{T}{2\pi r}$. We know there is a centripetal force due to gravity, so it follows: $\frac{Mv^2}{r}=\frac {GM^2}{r^2}$ Using these relationships, we find: $\frac{r}{GM^2}=\frac{T^2}{m4\pi^2 r^2}$ This simplifies to: $T^2 = \frac{4\pi^2r^3}{GM}$