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JEE MainPhysicsGravitation

Two satellites A and B are revolving in circular orbits around a planet. The orbital speed of satellite A is twice the orbital speed of satellite B . If the time period of satellite A is T , then the time period of satellite B will be

Options

  1. A4T
  2. B8T
  3. C2T
  4. DT 8

Correct answer

B. 8T

Step-by-step solution

The orbital speed of a satellite is given by v = GM R , which implies R 1 v^2 . According to Kepler's Third Law, the time period T is related to the orbital radius R by T^2 R^3 . Substituting the proportionality for R into Kepler's law: T^2 ( 1 v^2 )^3 T^2 1 v^6 T 1 v^3 We are given that v_A = 2v_B , and T_A = T . Taking the ratio of the time periods of B and A : T_B T_A = ( v_A v_B )^3 T_B T = (2)^3 = 8 T_B = 8T Answer: 8T

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