A scientific probe is in a stable circular orbit at a distance of 2R 2R\,2R from the centre of a spherical planet of radius R R\,R and uniform density ρ\rhoρ. The orbital speed of the probe is vvv.
What is the mean density ρ \rho\,ρ of the planet?
3v24πGR2\frac{3v^2}{4\pi G R^2}4πGR23v2
3v22πGR2\frac{3v^2}{2\pi G R^2}2πGR23v2
3v2πGR2\frac{3v^2}{\pi G R^2}πGR23v2
9v24πGR2\frac{9v^2}{4\pi G R^2}4πGR29v2
