A-LevelPhysicsGravitational fields9702/41 · May/June 2017 · Q19 Marks
Explain how a satellite may be in a circular orbit around a planet.
- (a)Explain how a satellite may be in a circular orbit around a planet.[2]
- (b)The Earth and the Moon may be considered to be uniform spheres that are isolated in space. The Earth has radius R and mean density ρ. The Moon, mass m, is in a circular orbit about the Earth with radius nR, as illustrated in Fig. 1.1. [Figure 1.1] The Moon makes one complete orbit of the Earth in time T. Show that the mean density ρ of the Earth is given by the expression ρ = 3πη³/GT²[4]
- (c)The radius R of the Earth is 6.38 × 10³ km and the distance between the centre of the Earth and the centre of the Moon is 3.84 × 10⁵ km. The period T of the orbit of the Moon about the Earth is 27.3 days. Use the expression in (b) to calculate ρ.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] gravitational force (of attraction between satellite and planet)
- [B1] provides / is centripetal force (on satellite about the planet)
- [B1] M = (4/3) × πR³ρ
- [B1] ω = 2π / T or v = 2πηR / T
- [M1] GMm / (nR)² = mnRω² or mv²/nR
- [A1] substitution clear to give ρ = 3πη³ / GT²
- [C1] n = (3.84 × 10⁵) / (6.38 × 10³) = 60.19 or 60.2
- [C1] ρ = 3π × 60.19³ / [(6.67 × 10⁻¹¹) × (27.3 × 24 × 3600)²]
- [A1] ρ = 5.54 × 10³ kg m⁻³
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