A spherical planet of radius R R\,R has a uniform density ρ\rhoρ. A satellite orbits the planet in a circular path of radius approximately equal to R R\,R with an orbital speed vvv.
What is the mean density ρ \rho\,ρ of the planet?
3v24πGR2\frac{3v^2}{4\pi G R^2}4πGR23v2
3v4πGR\frac{3v}{4\pi G R}4πGR3v
4πGR23v2\frac{4\pi G R^2}{3v^2}3v24πGR2
3v2R24πG\frac{3v^2 R^2}{4\pi G}4πG3v2R2
