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Robust resolution of Kepler’s equation in all eccentricity regimes

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Abstract

In this paper we discuss the resolution of Kepler’s equation in all eccentricity regimes. To avoid rounding off problems we find a suitable starting point for Newton’s method in the hyperbolic case. Then, we analytically prove that Kepler’s equation undergoes a smooth transition around parabolic orbits. This regularity allows us to fix known numerical issues in the near parabolic region and results in a non-singular iterative technique to solve Kepler’s equation for any kind of orbit. We measure the performance and the robustness of this technique by comprehensive numerical tests.

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Correspondence to Davide Farnocchia.

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Farnocchia, D., Cioci, D.B. & Milani, A. Robust resolution of Kepler’s equation in all eccentricity regimes. Celest Mech Dyn Astr 116, 21–34 (2013). https://doi.org/10.1007/s10569-013-9476-9

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  • DOI: https://doi.org/10.1007/s10569-013-9476-9

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