Kepler's Laws of Planetary Motion - Relation To Newton's Laws

Relation To Newton's Laws

Isaac Newton computed in his Philosophiæ Naturalis Principia Mathematica the acceleration of a planet moving according to Kepler's first and second law.

1. The direction of the acceleration is towards the Sun.
2. The magnitude of the acceleration is in inverse proportion to the square of the distance from the Sun.

This suggests that the Sun may be the physical cause of the acceleration of planets.

Newton defined the force on a planet to be the product of its mass and the acceleration. (See Newton's laws of motion). So:

1. Every planet is attracted towards the Sun.
2. The force on a planet is in direct proportion to the mass of the planet and in inverse proportion to the square of the distance from the Sun.

Here the Sun plays an unsymmetrical part which is unjustified. So he assumed Newton's law of universal gravitation:

1. All bodies in the solar system attract one another.
2. The force between two bodies is in direct proportion to the product of their masses and in inverse proportion to the square of the distance between them.

As the planets have small masses compared to that of the Sun, the orbits conform to Kepler's laws approximately. Newton's model improves Kepler's model and gives better fit to the observations. See two-body problem.

A deviation of the motion of a planet from Kepler's laws due to attraction from other planets is called a perturbation.