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Derive the inverse square of Newtown

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11th

Physics

Gravitation

Newton's Law of Gravitation

Newton's inverse square law...

PHYSICS

Asked on January 17, 2020 byYogesh Chirag

Newton's inverse square law is deduced from Kepler's ____ of planetary motion.

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Newton's inverse square law states that gravitational attraction force  between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The Newton's inverse square law is deduced from Kepler's 'Third law' of planetary motion. Kepler saw that planets move around in an elliptical orbit. 

Centripetal force on planet is calculated as :

F = rmv2 = rm(T2πR)2 = rT24π2mr2

F = r24π2mT2r3

But from Kepler's law,   T2r3 is constant for planets

Therefore F =  r24π2m i.e K  = r2G

From this the square inverse nature of gravitational force was derived by Newton.

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Answer 2

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The Newton's inverse square law is deduced from Kepler's 'Third law' of planetary motion. Kepler saw that planets move around in an elliptical orbit. From this the square inverse nature of gravitational force was derived by Newton.