Eccentric anomaly

Encyclopedia : E : EC : ECC : Eccentric anomaly

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The eccentric anomaly is the angle between the direction of periapsis and the current position of an object on its orbit, projected onto the ellipse's circumscribing circle perpendicularly to the major axis, measured at the centre of the ellipse. In the diagram below, it is E (the angle zcx).

Calculation

In astrodynamics eccentric anomaly E can be calculated as follows:

[E=\arccos }]

or equivalently

[\tan = \sqrt \tan.\,]

The relations between the radius (position vector magnitude) and the anomalies are:

[r = a \left ( 1 - e \cdot \cos \right )\,\!]

and

[r = a)}.\,\!]

See also

• Kepler's laws of planetary motion
• Mean anomaly
• True anomaly

References

• Murray, C. D. & Dermott, S. F. 1999, Solar System Dynamics, Cambridge University Press, Cambridge.
• Plummer, H.C., 1960, An Introductory treatise on Dynamical Astronomy, Dover Publications, New York. (Reprint of the 1918 Cambridge University Press edition.)

 

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