13.4b Ex4 MJ19 P41 Q1 Spacecraft Approach Orbit | A2 G-Fields | Cambridge A Level Physics

Example 5 - 9702/41/M/J/19: (a) 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. #9702s19p41 #A2orbitalMechanicsP4 #Lv3
(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 × 10^23 kg. The radius of the planet is 3.4 × 10^6 m.
(i) The spacecraft is to orbit the planet at a height of 2.4 × 105 m 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 x 10^3 ms-1.
(ii) One possible path of the spacecraft as it approaches the planet is shown in Fig. 1.1. The spacecraft enters the orbit at point A with speed 3.7 × 10^3 m s-1. At point B, a distance of 5.00 × 10^7 m from the centre of the planet, the spacecraft has a speed of 4.1 × 10^3 m s-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 × 10^9 J
(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.
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