Some Properties of Ellipses

Since the orbits of the planets are ellipses, let us review a few of their basic properties:

1. In an ellipse there are two points called foci (singular:focus) such that the sum of the distances to the foci from any point on the ellipse is a constant. In terms of the adjacent diagram, with "x" marking the location of the foci, we have the equation

a + b = constant

that defines the ellipse in terms of the distances a and b.

2. The amount of "flattening" of the ellipse is termed the eccentricity. Thus, in the following figure the ellipses become more eccentric from left to right. A circle may be viewed as a special case of an ellipse with zero eccentricity, while as the ellipse becomes more flattened the eccentricity approaches one. Thus, all ellipses have eccentricities lying between zero and one.

3. The long axis of the ellipse is called the major axis, while the short axis is called the minor axis (adjacent figure). Half of the major axis is termed a semimajor axis and half of the minor axis is termed the semiminor axis. The length of a semimajor axis is often termed the size of the ellipse.

It can be shown that the average separation of a planet from the Sun as it goes around its elliptical orbit is equal to the length of the semimajor axis. Thus, by the "radius" of a planet's orbit one usually means the length of the semimajor axis. For a more detailed investigation of the properties of ellipses, see this Java applet.