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Derive Newton's law of gravitation from …

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Derive Newton's law of gravitation from Kepler's third law of planetary motion

Posted by Madhav Chib 6 years, 10 months ago

CBSE > Class 11 > Physics

1 answers

Hi Bju 6 years, 10 months ago

F=mv^2/r But orbital vel is v=circumference/time=2πr/T By putting value of v in first eqn we get F=m/r*(2πr/T)^2=4π^2mr/T^2 Now by putting Kepler's law T^2=kr^3in above eqn we get F=4π^2mr/kr^3 As the force b/w the sun and the planets is mutual,it should also be proportional to the mass M of the sun. 4π^2/k is proportional to M so, 4π^2/k=GM So F=GMm/r^2

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