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JEE MainPhysicsGravitation

A satellite is revolving in a stable circular orbit around the Earth. Due to a small orbital adjustment, its orbital radius is decreased by 2 % . The percentage change in the time period of the satellite is

Options

  1. ADecreases by 4 %
  2. BDecreases by 1.33 %
  3. CIncreases by 3 %
  4. DDecreases by 3 %

Correct answer

D. Decreases by 3 %

Step-by-step solution

According to Kepler's Third Law, the time period T of a satellite is related to its orbital radius R as: T^2 R^3 T R^ 3/2 Taking the natural logarithm on both sides, we get: T = 3 2 R + constant Differentiating for small changes, we obtain: T T = 3 2 R R Given that the orbital radius decreases by 2 % , we have R R = -2 % . Substituting this value: T T = 3 2 (-2 %) = -3 % The negative sign indicates a decrease. Therefore, the time period decreases by 3 % . Answer: Decreases by 3 %

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