Question

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

Answer 1

The in Kepler's 3rd law refers to the length of the semi-major axis of a planet's ellipse. Newton was able to show in his Principia, published in 1687, that this law comes about as a natural consequence of his laws of motion and his law of gravity.


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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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