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Efficient inverse solution of Kepler's equationA bicubic polynomial approximation to Kepler's equation for elliptic orbits is shown to provide accurate starting values for efficient numerical solution of this equation for eccentric anomaly. In the approximate equation, a cubic in mean anomaly is set equal to a cubic in eccentric anomaly. The coefficients in the two cubics are obtained as functions of eccentricity by specifying values of function and slope at the midpoint and the endpoint of the complete interval (0 to pi). The initial estimate of eccentric anomaly to use in an iteration formula is obtained by evaluating the cubic in mean anomaly and finding the single real root of the cubic in eccentric anomaly. Numerical results are presented which indicate that the estimate accuracy of this method is roughly an order of magnitude better than that of other recently-reported formulas.
Document ID
19870047519
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Boltz, Frederick W.
(NASA Ames Research Center Moffett Field, CA, United States)
Date Acquired
August 13, 2013
Publication Date
December 1, 1986
Publication Information
Publication: Journal of the Astronautical Sciences
Volume: 34
ISSN: 0021-9142
Subject Category
Numerical Analysis
Accession Number
87A34793
Distribution Limits
Public
Copyright
Other

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