Newton's Law of gravitation using kepler's laws.

AI Thread Summary
The discussion focuses on deriving Newton's Law of Gravitation from Kepler's laws of planetary motion. The user attempts to solve the equations related to Kepler's laws, specifically using the equation for the radius in terms of eccentricity and angle. They arrive at a second time derivative of the radius, which leads to a form resembling Newton's law after accounting for centrifugal acceleration. However, the user expresses confusion regarding the origin of the centrifugal acceleration in their derivation. Clarification on this point is sought from other participants in the discussion.
Sourabh N
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Homework Statement



Derive Newton's Law of gravitation using kepler's laws.

Homework Equations



Kepler's law equations.
etc.

The Attempt at a Solution



l= r(1- e*cos(theta)) l- const. e- eccentricity
Solving these equations using kepler's laws (r^2(d(theta)/dt), etc.)

second time derivative of r = -4c^2/(lr^2) + 4c^2/r^3
subtracting centrifugal acc. (4c^2/r^3) from it I get Newton's law.

But I don't know how the centrifugal acc. come here.
 
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