Define gravitational potential at a point in terms of the work done.
The gravitational potential $\phi$ at distance $r$ from point mass $M$ is given by the expression $\phi = -\frac{GM}{r}$, where $G$ is the gravitational constant. Explain what the negative sign in this expression means.
A spherical planet may be treated as an isolated point mass with all its mass concentrated at the centre. A small mass $m$ is moving close to, and normal to, the surface of the planet. The mass moves away from the planet through a short distance $h$. State and explain why the change in gravitational potential energy $\Delta E_p$ of the mass is given by the expression $\Delta E_p = mgh$, where $g$ is the acceleration of free fall.
The planet in (c) has mass $M$ and diameter $6.8 \times 10^3\,\text{km}$. For this planet, the product $GM$ is $4.3 \times 10^{13}\,\text{N m}^2\,\text{kg}^{-1}$. A rock, initially at rest a long distance from the planet, accelerates towards the planet. Assuming that the planet has negligible atmosphere, calculate the speed of the rock as it hits the surface of the planet.