Eccentric Anomaly

In celestial mechanics, the eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit.

For the point P orbiting around an ellipse, the eccentric anomaly is the angle E in the figure. It is determined by drawing a vertical line from the major axis of the ellipse through the point P and locating its intercept P′ with the auxiliary circle, a circle of radius a (the semi-major axis of the ellipse) that enscribes the entire ellipse. This intersection P′ is called the corresponding point to P. The radius of the auxiliary circle passing through the corresponding point makes an angle E with the major axis.

The eccentric anomaly is one of three angular parameters ("anomalies") that define a position along an orbit; the other two being the true anomaly and the mean anomaly.