For a planet in a circular orbit of radius R around the same central star, how does orbital period T depend on R?
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Question

For a planet in a circular orbit of radius R around the same central star, how does orbital period T depend on R?

G1 Physics · Accepted Answer

Step 1: Gravitational attraction supplies centripetal force: GMm/R² = mv²/R. Step 2: Therefore v = √(GM/R). Step 3: T = 2πR/v = 2π√(R³/(GM)). Step 4: For a fixed central mass M, T ∝ R³ᐟ² (Kepler's third law). Final answer: T ∝ R³ᐟ² (Option B).