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Manipal MET2015PhysicsGravitation

For a given density of a planet, the orbital speed of satellite near the surface of the planet of radius R is proportional to

Options

  1. AR^ 1 / 2
  2. BR^ 3 / 2
  3. CR^ -1 / 2
  4. DR^0

Correct answer

D. R^0

Step-by-step solution

Applying Newton's second law to a circular orbit, we have m v^2 r = 4 ^2 r m T^2 = G M m r^2 where, m is the mass of satellite, and v is the orbital speed T is the time period T= 2 r^ 3 / 2 G M For r R and M= 4 3 R^3 ( = density of planet )T= 3 G i.e. T is independent of R

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