A line connecting the planet to the sun sweeps through equal areas in equal times

Conservation of angular momentum    is the reason for the equal areas.  As the radius increases, the speed of the planet decreases. 

It  is important to realize that the nature of the gravitational force is the reason for this law. Gravitational forces are CENTRAL FORCES pulling from center of mass to center of mass

Law 2: Equal Areas

Sir Isaac Newton was able to explain Kepler's Laws using his vast mathematical ability and his creation of the Universal Law of Gravitation!

Johannes Kepler   1571-1630

The square of the period of revolution is proportional to the cube of the average radius of revolution for each of the planets.

An ellipse has two focal points.  The sum of the two distances from a point on the ellipse to each of the focal points is a constant

The path of each planet is an ellipse with the sun at one of the focal points of the ellipse. 

Newton's Universal Law of Gravitation  is the reason planets follow elliptical paths.  Kepler formulated the law without knowing why it was true.

Special Forces

The Concept of Force

Law 1: Elliptical Orbits

link 1

link 2

link 3

ORBITS

Law 3: Law of Periods

The period of an object is the time for one complete cycle. 

Once  again it can be shown that the Universal Law of Gravitation can be used to product Kepler's Third Law!  Kepler's Laws are true because of the nature of the gravitational force as described by

 

Universal Gravitation

Kepler's Laws

The force of gravity between two masses is attractive, is directly proportional to the product of the masses and inversely proportional to the square of the distance from center to center of the masses.-- Newton's Universal Law of Gravitation

F = G (M1*M2)/r²