Define gravitational potential at a point in a gravitational field.
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 the centre.
A rock of mass $4.50\,\text{kg}$ lies on the Moon’s surface. Show that the change in gravitational potential energy of the rock as it is taken from the Moon’s surface to infinity is $1.27 \times 10^7\,\text{J}$.
The escape speed of the rock is the smallest speed it must be given at the Moon’s surface so that it can escape to infinity. Use the result in (i) to find the escape speed. Show your working.
The Moon in (b) 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).