A2 Daily A Level Physics question
Which statement must be true when an Earth satellite is moved from a circular orbit of radius R (measured from Earth’s centre) to a new circular orbit of radius 4R around the same planet? Compare (i) the orbital period and (ii) the area swept out by the radius vector from Earth’s centre in exactly one Earth day, after the move compared with before. Assume only Earth’s gravity acts.
Answer
The correct answer is D.
Correct: D — The period increases by a factor of 8; the area swept in one day doubles. For circular orbits about the same central body, T ∝ r^(3/2), so increasing radius by 4 makes T larger by 4^(3/2) = 8; the area swept in a fixed time is (1/2)r^2θ, with θ per day = 2π/T, so area per day ∝ r^2/T ∝ r^(1/2), which doubles when r is quadrupled. A The period does not scale as r; doubling T here confuses T ∝ r^(3/2), and the area per day does not halve because r^2/T increases with r. B Quadrupling T assumes T ∝ r, and saying the area per day is unchanged misapplies “equal areas in equal times” across different orbits (it applies within a single orbit). C The period factor 8 is correct, but claiming the area per day halves ignores the r^2 factor; since area/day ∝ r^(1/2), it increases, not decreases. D Uses T ∝ r^(3/2) to get 8, and area/day ∝ r^2/T to get a factor of 2, so this is consistent with Kepler’s laws.