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JEE MainPhysicsGravitation

Two identical satellites, A and B, are revolving in circular orbits around a planet. If the orbital angular momentum of satellite A is twice the orbital angular momentum of satellite B, the ratio of their time periods of revolution ( T_A T_B ) is :

Options

  1. A2 2
  2. B4
  3. C2
  4. D8

Correct answer

D. 8

Step-by-step solution

The orbital angular momentum of a satellite of mass m in a circular orbit of radius r is: L = mvr The orbital speed is given by v = GM r , where M is the mass of the planet. Substituting v into the expression for L : L = m GM r r = m GMr Since m , G , and M are constants, we have: L r r L^2 According to Kepler's Third Law, the time period T is related to the orbital radius r as: T^2 r^3 T r^ 3/2 Substituting r L^2 into the relation for T : T (L^2)^ 3/2 T L^3 Therefore, the ratio of the time periods is: T_A T_B = (

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