State the definition of gravitational potential at a point.
The Moon can be treated as an isolated sphere of radius $1.74 \times 10^{3}\ \text{km}$ with its mass of $7.35 \times 10^{22}\ \text{kg}$ concentrated at its centre.
A rock with mass $4.50\ \text{kg}$ is on the Moon’s surface. Show that the change in gravitational potential energy of the rock in moving it from the Moon’s surface to infinity is $1.27 \times 10^{7}\ \text{J}$.
Escape speed is the smallest speed that must be given to the rock when it is on the Moon’s surface so that it can escape to infinity. Use the answer in (i) to find the escape speed. Explain your working.
In (b), the Moon is assumed to be isolated in space. In reality, the Moon orbits the Earth. State and explain whether the minimum speed for the rock to reach the Earth from the Moon’s surface is different from the escape speed found in (b).