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Question: Answered & Verified by Expert
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., T2=Kr3.
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=GMmr2, here G is gravitational constant.
The relation between G and K is described as:
PhysicsGravitationNEETNEET 2015 (Phase 1)
Options:
  • A GK=4π2
  • B GMK=4π2
  • C K=G
  • D K=1G
Solution:
2764 Upvotes Verified Answer
The correct answer is: GMK=4π2

Here gravitational force is equal to centripetal force required for motion of planet.
Hence,
GMmr2=mv2r
v2=GMr
Time period is given by,
T=2πrv
T2=4π2r2v2
T2=4π2r2Gmr=4π2r3GM

We have given,
T2=kr3
On comparing,
k=4π2GMGMk=4π2

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