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 $122\,\text{kg}$ orbits Mars at a constant height of $1.7 \times 10^{6}\,\text{m}$ above the planet’s surface. The orbit is then raised to a height of $6.8 \times 10^{6}\,\text{m}$ above the surface. As a result, the satellite’s gravitational potential energy rises by $5.1 \times 10^{8}\,\text{J}$.
Show that the mass of Mars is $6.4 \times 10^{23}\,\text{kg}$.
Calculate the gravitational potential $\phi$ at the surface of Mars. Include a unit in your answer.
The satellite in (b) is shifted into an orbit in which it stays above the same point on Mars’s surface. The orbit has a period of $25$ hours. State what this tells you about Mars’s rotation on its axis.
State one other feature of this orbit.