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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

For an earth-satellite in a circular orbit, the time period is independent of

Options

  1. Athe mass of the earth
  2. Bthe universal gravitational constant
  3. Cthe radius of the orbit
  4. Dthe mass of the satellite

Correct answer

D. the mass of the satellite

Step-by-step solution

The gravitational force provides the necessary centripetal force for the satellite to move in a circular orbit. GMm r^2 = m ^2r GMm r^2 = m ( 2 T )^2r T^2 = 4 ^2r^3 GM T = 2 r^3 GM Here, M is the mass of the earth, r is the radius of the orbit, and G is the universal gravitational constant. The mass of the satellite m cancels out from both sides of the equation. Thus, the time period of an earth-satellite is independent of the mass of the satellite.

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