Two point masses are isolated in space and are separated by a distance x. State an expression relating the gravitational force F between the two masses to the magnitudes M and m of the masses. State the name of any other symbol used.

1. (a)State an expression relating the gravitational force F between the two masses to the magnitudes M and m of the masses. State the name of any other symbol used.[1]
2. (b)A spacecraft is to be put into a circular orbit about a spherical planet. The planet may be considered to be isolated in space. The mass of the planet, assumed to be concentrated at its centre, is 7.5 x 1023 kg. The radius of the planet is 3.4 × 106 m.
3. (b)(i)The spacecraft is to orbit the planet at a height of 2.4 × 105m above the surface of the planet. At this altitude, there is no atmosphere. Show that the speed of the spacecraft in its orbit is 3.7 × 103ms-1.[2]
4. (b)(ii)One possible path of the spacecraft as it approaches the planet is shown in Fig. 1.1. [Figure 1.1] The spacecraft enters the orbit at point A with speed 3.7 × 103ms-1. At point B, a distance of 5.00 × 107m from the centre of the planet, the spacecraft has a speed of 4.1 × 103ms¯¹. The mass of the spacecraft is 650 kg. For the spacecraft moving from point B to point A, show that the change in gravitational potential energy of the spacecraft is 8.3 x 10º J.[3]
5. (c)By considering changes in gravitational potential energy and in kinetic energy of the spacecraft, determine whether the total energy of the spacecraft increases or decreases in moving from point B to point A. A numerical answer is not required.[2]

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