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Optimal starters for solving the elliptic Kepler’s equation

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Abstract

In this paper starting algorithms for the iterative solution of elliptic Kepler’s equation are considered. New global efficiency measures to compare the quality of starters are introduced and several well known starters with minimum computational cost are analyzed on the light of these efficiency measures. New optimal starters with respect to these measures are derived. Finally we reconsider the highly accurate starter given by Markley in proposing an improvement of it for low to medium eccentricities.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, IUMA, Universidad de Zaragoza, 50009, Zaragoza, Spain

    M. Calvo, A. Elipe, J. I. Montijano & L. Rández

  2. Centro Universitario de la Defensa, 50090, Zaragoza, Spain

    A. Elipe

Authors
  1. M. Calvo
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  2. A. Elipe
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  3. J. I. Montijano
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  4. L. Rández
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Correspondence to A. Elipe.

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Calvo, M., Elipe, A., Montijano, J.I. et al. Optimal starters for solving the elliptic Kepler’s equation. Celest Mech Dyn Astr 115, 143–160 (2013). https://doi.org/10.1007/s10569-012-9456-5

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  • DOI: https://doi.org/10.1007/s10569-012-9456-5

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