If the distance between the Sun and Earth is doubled ,then the duration of the year on earth will be: [Given actual duration of the year = T ]

Step-by-step solution

According to Kepler's third law of planetary motion, the square of the time period T of a planet is directly proportional to the cube of the semi-major axis r of its orbit, which is given by T^2 r^3 . Let the initial distance be r₁ = r and the initial time period be T₁ = T . The new distance is r₂ = 2r . Using the relation T₂^2 T₁^2 = ( r₂ r₁ )^3 , we substitute the values: T₂^2 T^2 = ( 2r r )^3 = 2^3 = 8 . Taking the square root on both sides, we get T₂ T = 8 = 2 2 . Therefore, the new duration of the year is T₂ =