Question

explain how newton arrived at his law of gravitation from kepler's third law.

Answer 1

Isaac Newton computed in his Philosophiæ Naturalis Principia Mathematica the acceleration of a planet moving according to Kepler's first and second law. ... The magnitude of the acceleration is inversely proportional to the square of the planet's distance from the Sun (the inverse square law).

Answer 2

Answer:

Kepler's laws and Newton's laws taken together imply that the force that holds the planets in their orbits by continuously changing the planet's velocity so that it follows an elliptical path is

(1) directed toward the Sun from the planet,

(2) is proportional to the product of masses for the Sun and planet, and

(3) is inversely proportional to the square of the planet-Sun separation. This is precisely the form of the gravitational force, with the universal gravitational constant G as the constant of proportionality.

Thus, Newton's laws of motion, with a gravitational force used in the 2nd Law, imply Kepler's Laws, and the planets obey the same laws of motion as objects on the surface of the Earth.

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