A-LevelPhysicsGravitational fields9702/43 · May/June 2017 · Q19 Marks
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. Moon nR Earth radius R [Figure 1.1] The Moon makes one complete orbit of the Earth in time T.
- (a)Explain how a satellite may be in a circular orbit around a planet.[2]
- (b)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. ρ = .............................................. kg m⁻³ [3][3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
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 = 2πnR / 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
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →