Question

how Newton derivate his laws from Kepler?

second laws of motion?

Law of Gravitation?

Answer 1

Newton's law of gravitation from Kepler's law :

We can start with Kepler's third law that the square of the time period varies directly with the cube of the distance.

  

     , a constant. ------------ (1)

For an object describing circular motion, we can write a couple equations:

-------------- (2)

[ time = distance traveled ÷ velocity ]

and ----------- (3)

Putting (2) and (3) in (1) :

  

   ----------- (4)

This is all we can get from Kepler's law of motion. Since momentum is conserved, according to Newton's third law, the force acting on one mass by another would be equal and opposite to the force acting on the other mass by the first mass. Then, from (4) , it means, .