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

Show affiliations +
Journal:
Advances in the Astronautical Sciences

ISSN: 0065-3438

Year of publication: 2016

Volume: 156

Pages: 695-706

Type: Article

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

More publications in: Advances in the Astronautical Sciences

Related Projects

Métodos híbridos de propagación de órbitas basados en modelos de series temporales e inteligencia computacional aplicado a Space Situational Awareness. Hybrid methods for orbit propagation based on statistical time series models and computational intelli

2015/00067/001

Abstract

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.