Question

write the three laws given by Kepler. how did they help Newton to arrive at the inverse square law of gravity?

Answer 1

The planets move in elliptical orbits. The sun sits at one of the foci.



The radius vector, measured from the sun to the planet has a very neat property. The area swept out by the radius vector, covers equal areas in equal times.



The period  of orbit is simple related to . ( is half of the major axis of the ellipse). It is that  is proportional to .

These laws seemed to describe the motion of the planets very accurately but since Newton hadn't given us classical mechanics, people were at a loss to come up with a reasonable explanation. In fact, Newton's three laws are not enough to explain Kepler's. You still have to figure out what the force is between the sun and a planet.

Answer 2

Kepler's three laws of planetary motion can be described as follows:

The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)

An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas)

The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)