# Kepler's Laws - Newton's Generalization Of Kepler's Laws, Applications Of The Generalized Forms Of Kepler's Laws

### sun planet planetary planets

Johannes Kepler made it his life's work to create a heliocentric (sun-centered) model of the solar system which would accurately represent the observed motion in the sky of the Moon and planets over many centuries. Models using many geometric curves and surfaces to define planetary orbits, including one with the orbits of the six known planets fitted inside the five perfect solids of Pythagoras, failed.

Kepler was able to construct a successful model with the earth the third planet out from the Sun after more than a decade of this trial and error. His model is defined by the three laws named for him. He published the first two laws in 1609 and the last in 1619. They are:

1. The orbits of the planets are ellipses with the Sun at one focus (F1) of the ellipse.
2. The line joining the Sun and a planet sweeps out equal areas in the planet's orbit in equal intervals of time.
3. The squares of the periods of revolution "P" (the periods of time needed to move 360°) around the Sun for the planets are proportional to the cubes of their mean distances from the Sun. This law is sometimes called Kepler's Harmonic Law. For two planets, planet A and planet B, this law can be written in the form:

A planet's mean distance from the Sun (a) equals the length of the semi-major axis of its orbit around the Sun.

Kepler's three laws of planetary motion enabled him and other astronomers to successfully match centuriesold observations of planetary positions to his heliocentric solar system model and to accurately predict future planetary positions. Heliocentric and geocentric (Earth-centered) solar system models which used combinations of off-center circles and epicycles to model planetary orbits could not do this for time intervals longer than a few years; discrepancies always arose between predicted and observed planetary positions.