A moon of mass M and radius R orbits a planet of mass 3M and radius 2R. At a particular time, the distance between their centres is D, as shown in Fig. 2.1. Point P is a point along the line between the centres of the planet and the moon, at a variable distance x from the centre of the planet. The variation with x of the gravitational potential φ at point P, for points between the planet and the moon, is shown in Fig. 2.2. [Figure 2.1] [Figure 2.2] [Figure 2.3]

1. (a)State the relationship between gravitational potential and gravitational field strength.[2]
2. (b)(i)Explain why φ is negative throughout the entire range x = 2R to x = D – R.[3]
3. (b)(ii)One of the features of Fig. 2.2 is that φ is negative throughout. Describe two other features of Fig. 2.2.[2]
4. (b)(iii)On Fig. 2.3, sketch the variation with x of the gravitational field strength g at point P between x = 2R and x = D – R.[3]

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