If a planet has a satellite of mass $m$, orbital period $T$, and orbital radius $R$, the mass of the

Question

If a planet has a satellite of mass $m$, orbital period $T$, and orbital radius $R$, the mass of the planet $M$ can be calculated using which of the following expressions?

Professor PC Thomas Classes · Answer

The centripetal force is provided by the gravitational force: $\frac{GMm}{R^2} = m\omega^2 R$. Substituting $\omega = \frac{2\pi}{T}$, we get $\frac{GM}{R^2} = \frac{4\pi^2 R}{T^2}$, which gives $M = \frac{4\pi^2 R^3}{G T^2}$.