Kepler's First Law

The orbit of each planet is an ellipse with the Sun at one focus.

An ellipse is defined as the locus of all points such that the sum of the distances from two foci to any point on the ellipse is a constant. Below we see the elliptical orbit of a planet, P, with the Sun, S, at one of the foci. The other focus, F, is often called the empty focus. From the definition of an ellipse, we know that

r + r´ = 2a

[NMSU, N. Vogt]

Recall the equation for an ellipse in Cartesian coordinates:

(x/a)2 + (y/b)2 = 1

This reduces to the equation of a circle when a = b. We define the following properties of the ellipse.