A2 Daily A Level Physics question
An Earth‑observation satellite is moved from a circular orbit of radius r (measured from Earth’s centre) to a new circular orbit of radius 2r, with both orbits otherwise stable. Neglect air resistance. Which statement best describes how its orbital speed changes?
Answer
The correct answer is D.
Correct: D — It becomes about 0.71 of the original (a factor 1/√2); the reduced pull (∝1/r²) balances v²/r, so v falls with 1/√r. A is wrong because doubling radius does not halve the speed; from v ∝ 1/√r, v2/v1 = √(r/2r) = 1/√2 ≈ 0.71, not 0.5. B is wrong because although gravity is four times weaker, speed does not scale directly with g; equating the inward pull to the circular motion requirement gives v ∝ 1/√r, not 1/r². C is wrong because the weaker gravity at larger r cannot be ‘balanced’ by a larger path to keep v unchanged; the necessary centripetal acceleration is smaller, so the speed must decrease. D is correct since equating the inverse‑square pull to the v²/r requirement gives v2/v1 = √(r/2r) = 1/√2 ≈ 0.71.