Question

Deduce Newton's law of gravitation from Kepler's laws.

Answer 1

Kepler's 2nd law says that a line connecting the sun and an orbiting planet would sweep across an equal area of space in the same amount of time

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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