(a)[2]
Explain why the gravitational potential close to a point mass is negative.
(b)
A planet may be modelled as a uniform sphere. At distance $r$ from the planet’s centre, it has gravitational potential $\phi$. Figure 1.1 shows how $\phi$ varies with $\frac{1}{r}$.
(b(i))[2]
Show that the planet’s mass is $8.8 \times 10^{25}\,\text{kg}$.
(b(ii))[3]
The planet’s rotation period is $0.72$ Earth days. A satellite orbiting the planet stays above the same point on the planet’s surface. Use the mass of the planet in (b)(i) to determine the orbital radius $R$ of the satellite.
(b(iii))[3]
The speed of the satellite in (b)(ii) is $8400\,\text{m s}^{-1}$. The satellite’s mass is $1200\,\text{kg}$. Determine the extra energy needed to move the satellite from its orbit to infinity.