If a planet's orbital radius doubles, how does its orbital period change according to Kepler's Third Law?

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Multiple Choice

If a planet's orbital radius doubles, how does its orbital period change according to Kepler's Third Law?

Explanation:
Kepler's Third Law relates the orbital period to the semi-major axis as P^2 ∝ a^3. If the orbital radius doubles (a' = 2a), then P'^2 ∝ (2a)^3 = 8a^3, so P' ∝ sqrt(8) P = 2√2 P ≈ 2.83 P. Therefore the period increases by about 2.83 times. This assumes the central mass stays the same and the planet's mass is negligible.

Kepler's Third Law relates the orbital period to the semi-major axis as P^2 ∝ a^3. If the orbital radius doubles (a' = 2a), then P'^2 ∝ (2a)^3 = 8a^3, so P' ∝ sqrt(8) P = 2√2 P ≈ 2.83 P. Therefore the period increases by about 2.83 times. This assumes the central mass stays the same and the planet's mass is negligible.

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