Ellipse

Eccentricity

Semi-Major and Semi-Minor Axis

The semi-major and semi-minor axis (sometimes called together as the semiparameters) are axis perpendicular and intersected at the center of the ellipse.

Let \(a\) be the length of the semi-major axis and \(b\) be the length of the semi-minor axis:

\[\begin{split} a = r\frac{1 + e\cos{\nu}}{1+e^2}\\ b = r\frac{1 + e\cos{\nu}}{1-e^2}\\ \frac{b}{a} = \sqrt{1-e^2} \end{split}\]

• \(\nu\) : True anomaly