Give the definition of gravitational potential at a point.
An isolated solid sphere of radius $r$ can be treated as having its mass $M$ concentrated at its centre. The magnitude of the gravitational potential at the sphere’s surface is $\phi$.\n\nOn Fig. 1.1, indicate how the gravitational potential varies with distance $d$ from the centre of the sphere for $d$ ranging from $d = r$ to $d = 4r$.
The sphere in (b) is a planet with radius $r$ of $6.4 \times 10^6\,\text{m}$ and mass $M$ of $6.0 \times 10^{24}\,\text{kg}$. It is assumed that the planet has no atmosphere. A rock of mass $3.4 \times 10^3\,\text{kg}$ moves directly towards the planet. Its distance from the centre of the planet changes from $4r$ to $3r$. Calculate the change in gravitational potential energy of the rock.
Explain whether the rock’s speed increases, decreases or remains unchanged.