The Earth has mass M, radius R and mean density ρ, and the Moon is in a circular orbit of radius nR about the Earth with period T, where ρ = 3πn³/(GT²).

The radius R of the Earth is 6.38 × 10⁶ m and the distance between the centre of the Earth and the centre of the Moon is 3.84 × 10⁸ m.

The period T of the orbit of the Moon about the Earth is 27.3 days.

Use the expression in (b) to calculate ρ.