Physics 9702/43 — May/June 2017

Explain how a satellite may be in a circular orbit around a planet.

The Earth and the Moon may be considered to be uniform spheres that are isolated in space.
The Earth has radius $R$ and mean density $\rho$. The Moon, mass $m$, is in a circular orbit about
the Earth with radius $nR$, as illustrated in Fig. 1.1.

The Moon makes one complete orbit of the Earth in time $T$.
Show that the mean density $\rho$ of the Earth is given by the expression

The radius $R$ of the Earth is $6.38 \times 10^3\ \text{km}$ and the distance between the centre of the Earth
and the centre of the Moon is $3.84 \times 10^5\ \text{km}$.
The period $T$ of the orbit of the Moon about the Earth is $27.3$ days.
Use the expression in (b) to calculate $\rho$.

$\rho$ = ______ $\text{kg m}^{-3}$