Abstract
A new approach to solve Kepler’s equation based on the use of implicit functions is proposed here. First, new upper and lower bounds are derived for two ranges of mean anomaly. These upper and lower bounds initialize a two-step procedure involving the solution of two implicit functions. These two implicit functions, which are non-rational (polynomial) Bézier functions, can be linear or quadratic, depending on the derivatives of the initial bound values. These are new initial bounds that have been compared and proven more accurate than Serafin’s bounds. The procedure reaches machine error accuracy with no more that one quadratic and one linear iterations, experienced in the “tough range”, where the eccentricity is close to one and the mean anomaly to zero. The proposed method is particularly suitable for space-based applications with limited computational capability.
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The authors would like to thank Rose Sauser for checking and improving the use of English in the manuscript.
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Mortari, D., Elipe, A. Solving Kepler’s equation using implicit functions. Celest Mech Dyn Astr 118, 1–11 (2014). https://doi.org/10.1007/s10569-013-9521-8
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DOI: https://doi.org/10.1007/s10569-013-9521-8