What is meant by gravitational potential at a point?
Treat the Earth as a uniform sphere of radius $6.4 \times 10^{6}\,\text{m}$, with all of its mass $6.0 \times 10^{24}\,\text{kg}$ concentrated at the centre. A satellite of mass $2.4 \times 10^{3}\,\text{kg}$ is sent from the Equator and inserted into an equatorial orbit at a height of $5.6 \times 10^{6}\,\text{m}$ above the Earth’s surface.
Calculate the change $\Delta E_{p}$ in gravitational potential energy for the satellite as it moves from the Earth’s surface to its equatorial orbit.
Determine the satellite’s speed while it is in orbit.
The satellite’s speed at the Equator before launch, caused by the Earth’s rotation, is $470\,\text{m s}^{-1}$. Explain why the energy needed to launch it changes depending on whether, in orbit, it is travelling from west to east or from east to west.