Anomaly

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Anomaly

1. In general, a deviation from the norm.
2. In geodesy, a deviation of an observed value from a theoretical value, due to an abnormality in the observed quantity.
3. In celestial mechanics, the angle between the radius vector to an orbiting body from its primary (the focus of the orbital ellipse) and the line of apsides of the orbit, measured in the direction of travel, from the point of closest approach to the primary (perifocus).
The term defined above is usually called true anomaly v to distinguished it from the eccentric anomaly E which is measured at the center of the orbital ellipse to the projection of the body onto the auxiliary circle of the ellipse, or from the mean anomaly M which is what the true anomaly would become if the orbiting body had a uniform annular motion. The mean anomaly M can be computed by

M = n (t - T) where n is mean motion; t is time of the computation;

and T is time of perifocus. The eccentric anomaly E and the mean anomaly M are related by the Kepler equation

M = E - e sin E

where e is eccentricity of the ellipse. From E, the true anomaly v can be obtained by

<math> tan v/2=[(1+e)/(1-e)]1/2 tan E/2.</math>

References

This article is based on NASA's Dictionary of Technical Terms for Aerospace Use