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)? ( 2 = 1 . 4 )

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)? ( 2 = 1 . 4 ),

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 d a y s

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