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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=(x,y) on an ellipse with the equation the eccentric anomaly is the angle E such that 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. FormulasFrom the true anomalyThe eccentric anomaly can be computed from the true anomaly by the formulas where e is the eccentricity, hence where is the angular coordinate of point (X,Y) in polar coordinates. The following relation also holds: and hence From the mean anomalyThe eccentric anomaly E is related to the mean anomaly M by the formula This equation does not have a closed-form solution for E given M. It is usually solved by numerical methods, e.g. Newton-Raphson method. Radius and eccentric anomalyThe radius (distance from the focus of attraction to the orbiting body) is related to the eccentric anomaly by the formula From Wikipedia under the
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