Define gravitational potential at a specified point.
The Earth may be treated as an isolated sphere of radius $R$, with its mass concentrated at the centre. Fig. 1.1 shows how the gravitational potential $\phi$ changes with distance $x$ from the Earth’s centre. The Earth’s radius is $R = 6.4 \times 10^6\,\text{m}$.
Using the gravitational potential at the Earth’s surface, find a value for the Earth’s mass.
A meteorite is initially at rest at infinity. It then moves from infinity towards the Earth. Calculate the speed of the meteorite when it is a distance of $2R$ above the Earth’s surface. Explain your working.
In reality, the Earth is not an isolated sphere because it is orbited by the Moon, as shown in Fig. 1.2. Suggest two changes to the motion of the meteorite caused by the Moon.