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NEET2015PhysicsGravitationActual

Kepler's third law states that the square of the period of revolution (T) of a planet around the sun is proportional to the third power of the average distance r between sun and planet i.e., T 2 = K r 3 . Here K is constant. If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is F = G M m r 2 , here G is gravitational constant. The

Options

  1. AG K = 4 π 2
  2. BG M K = 4 π 2
  3. CK = G
  4. DK = 1 G

Correct answer

B. G M K = 4 π 2

Step-by-step solution

Here gravitational force is equal to centripetal force required for motion of planet. Hence, G M m r 2 = m v 2 r v 2 = G M r Time period is given by, T = 2 π r v T 2 = 4 π 2 r 2 v 2 T 2 = 4 π 2 r 2 G m r = 4 π 2 r 3 G M We have given, T 2 = k r 3 On comparing, k = 4 π 2 G M ⇒ G M k = 4 π 2

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