Suppose the gravitational force varies inversely as the nth power of distance .then the time period of a planet in circular orbit of radius R around the sun will be proportional to [AIEEE 2004]
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Suppose the gravitational force varies inversely as the nth power of distance .then the time period of a planet in circular orbit of radius R around the sun will be proportional to [AIEEE 2004]
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Explanation:- The necessary centripetal force required for a planet to move round the sun = Garvitational force exerted on it
Now., we know that ,
T = 2πR/V = 2πR × (Rⁿ⁻¹/GMₑ)^½ _____From (i)
⟹ 2π (R²×Rⁿ⁻¹ /GMₑ)^½
⟹ 2π (Rⁿ⁺¹ /GMₑ)^½
⟹ T∝ R(ⁿ⁺¹)/2 Answer