Kepler’s Laws of Planetary Motion Copyright 2001 by the Rector and Visitors of the University of Virginia

Kepler’s Laws of Planetary Motion Law 1 - Law of Ellipses Law 2 - Law of Equal Areas Law 3 - Harmonic Law (P2=ka3) Kepler’s laws provide a concise and simple description of the motions of the planets. Discovered in 1609.

Kepler’s 1st Law

Kepler’s 1st Law: “Law of Ellipses” Kepler’s 1st Law: “Law of Ellipses”. Each planet moves about the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse.

The major axis is the widest diameter of the ellipse. The semi-major axis is ½ this distance. -This is the average distance of the planet from the Sun. The eccentricity is a measure of the roundness of the ellipse: e=d/L. d is distance between the two focus points L is length of major axis

Kepler’s 1st Law An eccentricity of 0 is a perfect circle. An eccentricity near 1 is a very elongated ellipse.

Lunar Orbit of Explorer 35 Moon

Kepler’s 2nd Law

Kepler’s 2nd Law: “Law of Equal Areas” Kepler’s 2nd Law: “Law of Equal Areas”. The straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time.

Kepler’s 2nd Law (simplified) The orbital speed of a planet is the greatest when it is closest to the sun and the least when it is farthest from the sun.

Aphelion –the point in the orbit of an object (planet, asteroid, or comet) at which it is furthest from the sun Perihelion – the point in the orbit of an object at which it is closest to the sun.

Kepler’s 3rd Law: “law of harmonies” - compares the orbital period and radius of orbit of a planet to those of other planets.

Kepler’s 3rd Law (simplified) The closer a planet’s orbit is to the sun, the faster its speed and, therefore, the shorter its period of revolution (year). So inner planets travel faster than outer planets.