Define gravitational potential at a point in a gravitational field.
The Earth may be treated as an isolated sphere of radius $R$, with its mass concentrated at the centre. Figure 1.1 shows how gravitational potential $\phi$ varies with distance $x$ from the Earth’s centre.
By using the gravitational potential at the Earth’s surface, determine the mass of the Earth. Take the Earth’s radius $R$ to be $6.4 \times 10^6\,\text{m}$.
A meteorite is initially at rest at infinity. It moves from infinity towards the Earth. Calculate the speed of the meteorite when it is $2R$ above the Earth’s surface. Show your working.
In reality, the Earth is not an isolated sphere because the Moon orbits it, as shown in Fig. 1.2. The meteorite’s initial path is also drawn. Suggest two ways in which the Moon alters the meteorite’s motion.