Celestial Mechanics and Dynamical Astronomy

, Volume 79, Issue 4, pp 277–296 | Cite as

Short Term Evolution of Artificial Satellites

  • A. Abad
  • J. F. San-Juan
  • A. Gavín


When the elimination of the parallax and the elimination of the perigee is applied to the zonal problem of the artificial satellite, a one-degree of freedom Hamiltonian is obtained. The classical way to integrate this Hamiltonian is by applying the Delaunay normalization, however, changing the time to the perturbed true anomaly and the variable to the inverse of the distance, the Hamilton equations become a perturbed harmonic oscillator. In this paper we apply the Krylov—Bogoliubov—Mitropolsky (KBM) method to integrate the perturbed harmonic oscillator as an alternative method to the Delaunay normalization. This method has no problem with small eccentricities and inclinations, and shows good numerical results in the evaluation of ephemeris of satellites.

artificial satellite harmonic oscillators KBM method 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • A. Abad
    • 1
  • J. F. San-Juan
    • 2
  • A. Gavín
    • 1
  1. 1.Grupo de Mecánica EspacialUniversidad de ZaragozaZaragozaSpain
  2. 2.Universidad de La RiojaLogroñoSpain

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