Kepler's First Law, The Law of Orbits

Definition

All planets move in elliptical orbits, having the Sun at one focus.

The figure above describes an object with polar coordinates and moving in an elliptical orbit around the larger object, the sun.

We can describe the orbit itself using the semimajor axis , the longest radius of the ellipse, and the eccentricity , a measure of the flatness or roundness of the ellipse (For a circle, ).

The foci of the ellipse are the larger mass and . is the maximum distance from to and is the shortest, is also called the aphelion and is also called the perihelion or perigee.

Note that:

Most planets in the solar system have small eccentricities, so nearly circular orbits. For circular orbits, .