Define what is meant by gravitational potential at a point.
Mars may be treated as an isolated uniform sphere with radius $3.4 \times 10^{6}\,\text{m}$. A satellite of mass $122\,\text{kg}$ is in orbit around Mars at a constant height of $1.7 \times 10^{6}\,\text{m}$ above the surface of the planet. The orbit height is raised to $6.8 \times 10^{6}\,\text{m}$ above the surface. This increases the satellite’s gravitational potential energy by $5.1 \times 10^{8}\,\text{J}$.
Show that Mars’s mass is $6.4 \times 10^{23}\,\text{kg}$.
Calculate the gravitational potential $\phi$ at Mars’s surface. Include a unit in your answer.
The satellite in (b) is moved into an orbit so that it remains above the same point on Mars’s surface.
The orbit has a period of $25\,\text{hours}$. State what this tells you about Mars’s rotation on its axis.
State one additional characteristic of this orbit.