Eccentricity of an Ellipse

Tracing an ellipse with a pencil and a string of fixed length around two fixed pins illustrates a path where the combined distance to the pins remains constant.

This defines the geometry of an ellipse, while its shape depends on its eccentricity, e—the ratio of the focal distance to the semi-major axis length.

When e is zero, the ellipse is a perfect circle. As e increases, the ellipse stretches along the major axis.

This shape appears in orbital paths such as that of Halley’s Comet, which has an eccentricity of 0.967 and the Sun at one focus.

The major axis of the orbit measures approximately 35.88 astronomical units—a standard unit of measurement in astronomy.

To express Halley’s orbit in standard form, the ellipse is centered at the origin, with its major axis aligned along the x-axis.

Multiplying the semi-major axis by e gives the focal distance.

The semi-minor axis length is then calculated using the Pythagorean theorem, which relates it to the semi-major axis and the focal distance, completing the overall shape of the ellipse.

These values are substituted into the standard form to model the orbit.