Answer all the questions in the spaces provided. (b) A rocket is launched from the surface of a planet and moves along a radial path, as shown in Fig. 1.1. planet mass M A R R 4R Fig. 1.1 B rocket path The planet may be considered to be an isolated sphere of radius R with all of its mass M concentrated at its centre. Point A is a distance R from the surface of the planet. Point B is a distance 4R from the surface.

1. (a)Define gravitational potential at a point.[2]
2. (b)(i)Show that the difference in gravitational potential Δφ between points A and B is given by the expression Δφ = 3GM / 10R where G is the gravitational constant.[1]
3. (b)(ii)The rocket motor is switched off at point A. During the journey from A to B, the rocket has a constant mass of 4.7 × 10⁴ kg and its kinetic energy changes from 1.70 TJ to 0.88 TJ. For the planet, the product GM is 4.0 × 10¹⁴ Nm² kg⁻¹. It may be assumed that resistive forces to the motion of the rocket are negligible. Use the expression in (b)(i) to determine the distance from A to B.[3]

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