Abstract
We derive a new method to obtain an approximate solution for Kepler's equation. By means of an auxiliary variable it is possible to obtain a starting approximation correct to about three figures. A high order iteration formula then corrects the solution to high precision at once. The method can be used for all orbit types, including hyperbolic. To obtain this solution the trigonometric or hyperbolic functions must be evaluated only once.
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References
Burkhart, T.M. and Danby, J.M.A.: (1983),Cel. Mech.,31, 317–328.
Danby, J.M.A. and Burkhart, T.M.: (1983),Cel. Mech.,31, 95–107.
Herrick, S.: (1972),Astrodynamics, Vol.II, Van Nostrand Reinhold Company, London.
Neutch, W. and Schüfer, E.: (1986),Astroph. and Space Sci.,125, 77–83.
Odell, A. W. and Gooding, R.H.: (1986),Cel. Mech.,38, 307–334.
Stiefel, E.L. and Scheifele, G., (1971),Linear and Regular Celestial Mechanics, Springer, Berlin.
Siewert, C.E. and Burniston, E.E.: 1972),Cel. Mech.,6, 294–304.
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Mikkola, S. A cubic approximation for Kepler's equation. Celestial Mechanics 40, 329–334 (1987). https://doi.org/10.1007/BF01235850
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DOI: https://doi.org/10.1007/BF01235850