Paper 3 Gravitational Fields Drills

Q1 Gravitational potential and work

A spacecraft of mass $950\mathrm{kg}$ moves from distance $r_1=8.0\times 10^6\mathrm{m}$ to $r_2=1.6\times 10^7\mathrm{m}$ from Earth’s centre. Take Earth mass as $5.97\times 10^{24}\mathrm{kg}$.

1. Calculate the gravitational potential at $r_1$ and $r_2$. [3]
2. Calculate the change in gravitational potential energy of the spacecraft. [3]
3. State whether external work must be done on the spacecraft for this change, assuming no change in kinetic energy. [2]
4. Explain why gravitational potential is negative with the infinity reference. [2]

Q2 Geostationary orbit

A satellite is required to remain above the same point on Earth’s equator.

1. State three conditions for a geostationary orbit. [3]
2. Explain why the orbital plane must be equatorial. [2]
3. Using angular speed $\omega =2\pi /T$, show that orbital radius satisfies

$$r^3=\frac{GM}{{\omega }^2}.$$

[3] 4. Calculate the orbital radius using $T=8.64\times 10^4\mathrm{s}$ and $M=5.97\times 10^{24}\mathrm{kg}$. [3]