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NTA Abhyas JEE Main2020PhysicsGravitationPractice

A satellite of mass m orbits around the Earth of mass M in an elliptical orbit of semi-major and semi-minor axes 2 a and a respectively. The angular momentum of the satellite about the centre of the Earth is

Options

  1. Aπ m G M a 2
  2. Bπ m G M a 4
  3. Cm G M a 8
  4. Dm G M a 2

Correct answer

D. m G M a 2

Step-by-step solution

If the satellite was orbiting the Earth in a circular orbit of radius 2 a , then its time period would be T = 2 π 2 a 3 G M The same would be the time period of the satellite if it orbits in an ellipse having a semi-major axis 2 a The area of the ellipse is A = π × 2 a × a = 2 π a 2 d A d t = L 2 m = 2 π a 2 T , where L is the angular momentum of the satellite about the centre of the Earth. ⇒ L = 4 π m a 2 G M 2 π 8 a 3 = m G M a 2

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