State the connection between gravitational potential and gravitational field strength.
A moon of mass $M$ and radius $R$ revolves around a planet of mass $3M$ and radius $2R$. At a given moment, the separation between their centres is $D$, as shown in Fig. 2.1. Point $P$ lies on the line joining the centres of the planet and the moon, at a variable distance $x$ from the centre of the planet. Fig. 2.2 shows how the gravitational potential $\phi$ at point $P$ changes with $x$ for positions between the planet and the moon. (i) Explain why $\phi$ is negative across the whole interval $x = 2R$ to $x = D - R$. (ii) One feature of Fig. 2.2 is that $\phi$ remains negative throughout. Describe two other features of Fig. 2.2. (iii) On Fig. 2.3, sketch the way the gravitational field strength $g$ at point $P$ varies with $x$ between $x = 2R$ and $x = D - R$.
Explain why $\phi$ is negative across the whole interval $x = 2R$ to $x = D - R$.
One feature of Fig. 2.2 is that $\phi$ remains negative throughout. Describe two other features of Fig. 2.2.
On Fig. 2.3, sketch the way the gravitational field strength $g$ at point $P$ varies with $x$ between $x = 2R$ and $x = D - R$.