On solving a generalization of the kepler equation

  1. San-Juan, J.F. 3
  2. López, R. 1
  3. Hautesserres, D. 2
  1. 1 Centro de Investigación Biomédica de La Rioja
    info

    Centro de Investigación Biomédica de La Rioja

    Logroño, España

    ROR https://ror.org/03vfjzd38

  2. 2 Centre National D'Etudes Spatiales
    info

    Centre National D'Etudes Spatiales

    París, Francia

    ROR https://ror.org/04h1h0y33

  3. 3 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

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Libro:
Advances in the Astronautical Sciences. Spaceflight mechanics 2015 : proceedings of the 25th AAS/AIAA Space Flight Mechanics Meeting

ISBN: 978-0-87703-623-4

Año de publicación: 2015

Volumen: 155

Páginas: 3015-3029

Tipo: Capítulo de Libro

SCOPUS: 2-s2.0-85007346264 WoS: WOS:000371647200181 GOOGLE SCHOLAR

Resumen

In the context of general perturbation theories, the motion of an artificial satellite or space debris object around an Earth-like planet perturbed by the J(2) effect is analyzed. By means of two Lie transforms and the Krylov-Bogoliubov-Mitropolsky method, a first order theory in closed form of the eccentricity is produced. During the integration process it is necessary to solve a perturbed Kepler equation. In this work, the application of the numerical techniques and initial guesses used to solve the classical Kepler equation, or even the solution of Kepler equation itself, to the generalized equation is discussed.