Analytical approximations to the generalization of the Kepler equation

  1. López, R. 2
  2. San-Juan, J.F. 3
  3. Hautesserres, D. 1
  1. 1 Centre National D'Etudes Spatiales
    info

    Centre National D'Etudes Spatiales

    París, Francia

    ROR https://ror.org/04h1h0y33

  2. 2 Centro de Investigación Biomédica de La Rioja
    info

    Centro de Investigación Biomédica de La Rioja

    Logroño, España

    ROR https://ror.org/03vfjzd38

  3. 3 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

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Revista:
Advances in the Astronautical Sciences

ISSN: 0065-3438

Any de publicació: 2016

Volum: 156

Pàgines: 695-706

Tipus: Article

SCOPUS: 2-s2.0-85007322096 WoS: WOS:000387517700041 GOOGLE SCHOLAR

Altres publicacions en: Advances in the Astronautical Sciences

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Resum

The generalized Kepler equation is a transcendental non-linear equation which appears in the zonal problem of the artificial satellite theory when the Krylov-Bogoliubov-Mitropolsky method is employed. In this work, the Lie-Deprit method is used to apply Lagrange's inversion theorem in order to solve the generalized Kepler equation. For small eccentricities, the analytical approximate solution yields similarly accurate results to numerical methods. For the rest of eccentricities, we discuss the applicability of this approximation as an initial guess in the numerical method used to solve the generalized Kepler equation.