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KVPY2017PhysicsGravitation

A star of mass M (equal to the solar mass) with a planet (much smaller than the star) revolves around the star in a circular orbit. The velocity of the star with respect to the center of mass of the star-planet system is shown below: The radius of the planet's orbit is closest to (1 A. U. Earth-Sun distance)

Options

  1. A0.004 A. U .
  2. B0.008 A.U.
  3. C0.004 A.U.
  4. D0.12 A.U.

Correct answer

C. 0.004 A.U.

Step-by-step solution

T ²= 4 ² GM a ² 4 ² GM =1 ~T = in year a = radius in A.U. T =3 days = 3 365 year a = ( 3 365 )^ 2 / 3 a =0.04 A.U

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