(a)[2]
Explain how a satellite can move in a circular orbit around a planet.
(b)[4]
The Earth and the Moon can be treated as uniform spheres isolated in space. The Earth has radius $R$ and mean density $\rho$. The Moon, mass $m$, is in a circular orbit around the Earth with radius $nR$, as shown in Fig. 1.1. The Moon completes one full orbit of the Earth in time $T$. Show that the mean density $\rho$ of the Earth is given by the expression $\rho = \frac{3\pi n^3}{G T^2}$.
(c)[3]
The Earth’s radius $R$ is $6.38 \times 10^3\,\text{km}$ and the distance from the centre of the Earth to the centre of the Moon is $3.84 \times 10^5\,\text{km}$. The Moon’s orbital period $T$ about the Earth is $27.3$ days. Use the expression in \(b\) to calculate $\rho$.