If a new planet is discovered rotating around the sun with the orbital radius double that of earth, then what will be its time period (in earth's days)?

Question

If a new planet is discovered rotating around the sun with the orbital radius double that of earth, then what will be its time period (in earth's days)?, 1032, 1023, 1024, 1043

MARKS App · Accepted Answer

From Kepler's third law of planetary motion T 2 ∝ R 3 G i v e n , R p = 2 R e ∴ T e 2 T p 2 = R e 3 R p 3 ⟹ T e 2 T p 2 = R e 3 2 R e 3 ⟹ T p = 2 2 T e S i n c e , T e = 365 d a y s = 1 y e a r , w e h a v e T p = 2 2 × 365 d a y s T p = 1032.37 T P = 1032 d a y s

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