Define gravitational potential at a point in a gravitational field.
Explain why the gravitational potential at X has a negative value.
State an expression, in terms of $\Phi$, for the gravitational potential at Y caused by the planet.
Satellite $X$, with mass $M$, orbits a planet at a fixed distance $4R$ from the centre of the planet, as shown in Fig. 1.1. A second satellite $Y$, with mass $2M$, orbits the planet at orbital radius $R$. The gravitational potential at $X$ due to the planet is $-\Phi$. The planet is a uniform sphere.
Complete Table 1.1 by writing expressions, in terms of some or all of $M$, $R$ and $\Phi$, for the quantities shown for each of satellites $X$ and $Y$: • gravitational field strength at satellite due to planet • gravitational potential energy of satellite