Physics (AS & A Level) · Oct / Nov 2016 · Paper 41 · Question 1
9702
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A satellite is in a circular orbit of radius r about the Earth of mass M, as illustrated in Fig. 1.1. Earth mass M satellite r Fig. 1.1 The mass of the Earth may be assumed to be concentrated at its centre.
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1(a)[3]
gravitational force provides/is the centripetal force GMm / r 2 = mv 2 / r or GMm / r 2 = mrω2 and v = 2πr / T or ω = 2π / T with algebra to T 2 = 4π2r 3 / GM [3]
or acceleration due to gravity is the centripetal acceleration (B1) GM / r 2 = v 2 / r or GM / r 2 = rω2 and v = 2πr / T or ω = 2π / T (M1) with algebra to T 2 = 4π2r3 / GM (A1)
1(b)(i)[2]
equatorial orbit/orbits (directly) above the equator from west to east [2]
1(b)(ii)[2]
(24 × 3600) 2 = 4π2r 3 / (6.67 × 10–11 × 6.0 × 1024) r 3 = 7.57 × 1022 r = 4.2 × 107 m [2]
1(c)[2]
(T / 24) 2 = {(2.64 × 107) / (4.23 × 107)}3 = 0.243 T = 12 hours [2]
or k (= T 2 / r 3) = 242 / (4.23 × 107) 3 (B1) k = 7.61 × 10–21 T 2 (= kr 3) = 7.61 × 10–21 × (2.64 × 107) 3 = 140 T = 12 hours (A1)
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