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JEE MainPhysicsGravitation

Two planets A and B are orbiting a star in circular orbits. If the time period of revolution of planet A is 8 times the time period of planet B , then the ratio of the orbital radius of planet A to that of planet B is:

Options

  1. A4
  2. B8
  3. C2
  4. D16

Correct answer

A. 4

Step-by-step solution

According to Kepler's third law of planetary motion, the square of the time period of revolution is directly proportional to the cube of the orbital radius. T^2 R^3 ( R_A R_B )^3 = ( T_A T_B )^2 Given that T_A = 8 T_B , we have T_A T_B = 8 . Substituting this value, we get: ( R_A R_B )^3 = (8)^2 = 64 R_A R_B = (64)^ 1/3 = 4 Answer: 4

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