An asteroid of uniform density ρ \rho\,ρ is spherical. A scientific probe orbits the asteroid in a circular path at a distance extremely close to its surface.
If G G\,G is the gravitational constant, which expression gives the orbital period T T\,T of the probe?
3πGρ\sqrt{\frac{3\pi}{G\rho}}Gρ3π
34πGρ\sqrt{\frac{3}{4\pi G\rho}}4πGρ3
4π3Gρ\sqrt{\frac{4\pi}{3G\rho}}3Gρ4π
2π3Gρ2\pi\sqrt{\frac{3}{G\rho}}2πGρ3
