The Earth may be assumed to be an isolated uniform sphere with its mass of 6.0 × 10^24 kg concentrated at its centre. A satellite of mass 1200 kg is in a circular orbit about the Earth in the Earth's gravitational field. The period of the orbit is 94 minutes.
- (a)Define gravitational field strength.[1]
- (b)Calculate the radius of the orbit of the satellite. radius = ........................................................... m [3][3]
- (c)Rockets on the satellite are fired so that the satellite enters a different circular orbit that has a period of 150 minutes. The change in the mass of the satellite may be assumed to be negligible.
- (c)(i)Show that the radius of the new orbit is 9.4 × 10^6 m.[2]
- (c)(ii)State, with a reason, whether the gravitational potential energy of the satellite increases or decreases.[1]
- (c)(iii)Determine the magnitude of the change in the gravitational potential energy of the satellite. change in potential energy = .............................................................. J [3][3]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [1] (a) force per unit mass
- [1] (b) GMm/r² = mrω² and ω = 2π/Τ
- [1] GMm/r² = mv²/r and v = 2πr/T
- [1] 6.67 x 10^-11 × 6.0 × 10^24 = r³ × [2π / (94 × 60)]²
- [1] r = 6.9 × 10^6 m
- [1] (c)(i) r³ / T² = constant
- [1] r³ / (6.9 × 10^6)³ = (150 /94)² so r = 9.4 × 10^6 m
- [1] GMT²/4π² = r³ and clear that M is 6.0 × 10^24
- [1] 6.67 × 10^-11 × 6.0 × 10^24 = r³ × [2π / (150 × 60)]² so r = 9.4 x 10^6 m
- [1] (c)(ii) separation increases so (potential energy) increases
- [1] movement is against gravitational force so (potential energy) increases
- [1] (c)(iii) potential energy = (−)GMm / r
- [1] ΔΕΡ = 6.67 × 10–11 × 6.0 × 10^24 × 1200 × [(6.9 × 10^6)–1 – (9.4 × 10^6)–1]
- [1] = 1.9 × 10^10 J
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