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JEE MainPhysicsGravitation

A satellite is transferred from one circular orbit to another such that its orbital angular momentum about the center of the earth increases by 2 % . The approximate percentage change in its time period of revolution is

Options

  1. A6 %
  2. B3 %
  3. C4 %
  4. D1 %

Correct answer

A. 6 %

Step-by-step solution

The orbital angular momentum L of a satellite of mass m is given by L = mvr . Since the orbital speed is v = GM r , we can write: L = m ( GM r ) r = m GMr This implies that L r^ 1/2 , or equivalently, r L^2 . According to Kepler's third law, the time period T is related to the orbital radius r by T r^ 3/2 . Substituting r L^2 into the time period relation gives: T (L^2)^ 3/2 T L^3 For small percentage changes, we can use the binomial approximation: T T = 3 L L Given that the angular momentum increases by 2 % ( L L

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