Question

A small satellite revolves around a planet in an orbit just above planet's surface. Taking the mean density of the planet $8000$kg $m^{-3}$ and $G=6.67\times {10}^{-11}$N $m^{-2}/k{g}^{-2}$, find the time period of the satellite.

Answer 1

$\frac{GmM}{R^2}=\frac{{mv}^2}{R}v=\sqrt{\frac{GM}{R}}T=\frac{2\pi }{v}=2\pi \sqrt{\frac{3R}{G4\pi R^{3}8000}}$

$T=0.0065$Hz