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NTA Abhyas JEE Main2020PhysicsGravitationPractice

A planet moves around the sun (mass = M s ) in an elliptical orbit such that its minimum and maximum distance from the sun are r and R respectively. The period of revolution of this planet around the sun is

Options

  1. AT = π r + R 3 2 G M s
  2. BT = π r + R 3 3 G M s
  3. CT = π r + R 3 G M s
  4. DT = π 2 r + R 3 G M s

Correct answer

A. T = π r + R 3 2 G M s

Step-by-step solution

The length of the semi-major axis of the elliptical orbit of the planet is a = r + R 2 If we assume that there is a hypothetical planet which moves around the sun in a circular orbit of radius r 0 = r + R 2 , then the time period of this hypothetical planet and our given planet will be same. The time period of a planet around the sun in circular orbit is T = 2 π r 3 0 G M s = 2 π r + R 2 3 G M s T = π r + R 3 2 G M s

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