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Analytical Theory of Motion of a Mars Orbiter

  • J. F. San Juan
  • S. Serrano
  • A. Abad
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3039)

Abstract

The design of spatial missions to Mars requires the development of analytical theories in order to put artificial satellites in orbit around Mars.

In this paper, we present a complete third order analytical model of a satellite perturbed by the zonal J 2, ..., J 6 harmonics of the Mars potential. Two Lie transformations, the elimination of the Parallax and the elimination of the Perigee, and the Krylov–Bogoliubov–Mitropolsky method are applied to obtain a complete integration of the model. The algebraic expressions of the generators, the Hamiltonians and the integrals, together with a software code to compute the ephemeris of the satellite, are automatically obtained using our computer algebra system ATESAT.

References

  1. 1.
    Abad, A., San Juan, J.F.: PSPC: A Poisson Series Processor coded in C. In: Kurzynska, et al. (eds.) Dynamics and Astrometry of Natural and Artificial Celestial Bodies, pp. 383–389. Poznam, Poland (1993)Google Scholar
  2. 2.
    Abad, A., San Juan, J.F.: ATESAT: software tool for obtaining automatically ephemeris from analytical simplifications. In: Elipe, A., Paquet, P. (eds.) Conseil de L’Europe. Cahiers du Centre Européen de Géodynamique et de Séismologie, Luxembourg, vol. 10, pp. 93–98 (1995)Google Scholar
  3. 3.
    Abad, A., Elipe, A., Palacián, J., San Juan, J.F.: ATESAT: A Symbolic Processor for Artificial Satellite Theory. Mathematics and Computers in Simulation 45, 497–510 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Abad, A., San Juan, J.F., Gavín, A.: Short term evolution of artificial satellites. Celestial Mechanics and Dynamical Systems 79, 277–296 (2001)zbMATHCrossRefGoogle Scholar
  5. 5.
    Alfriend, K.T., Coffey, S.L.: Elimination of the Perigee in Satellite Problem. Celestial Mechanics 32, 163–172 (1984)zbMATHCrossRefGoogle Scholar
  6. 6.
    Bogoliubov, N.N., Mitropolsky, Y.A.: Asymptotic Method in the Theory of Nonlinear Oscillations. Gordon and Breach, New York (1961)Google Scholar
  7. 7.
    Deprit, A.: Canonical Transformations Depending on a Small Parameter. Celestial Mechanics 1, 12–30 (1969)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Deprit, A.: The Elimination of the Parallax in Satellite Theory. Celestial Mechanics 24, 111–153 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Desai, P.N., Braun, R.D., Powell, R.W.: Aspects of Parking Orbit Selection in a Manned Mars Mission, NASA TP-3256 (1992)Google Scholar
  10. 10.
    Henrard, J.: On a perturbation theory using Lie Transform. Celestial Mechanics 3, 107–120 (1970)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Kamel, A.A.: Perturbation methods in the theory of nonlinear oscillations. Celestial Mechanics 3, 90–106 (1970)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Krylov, N., Bogoliubov, N.N.: Introduction to Nonlinear Mechanics. Princeton University Press, Princeton (1947)Google Scholar
  13. 13.
    San Juan, J.F.: ATESAT: Automatization of theories and ephemeris in the artificial satellite problem, Tech. rep. CT/TI/MS/MN/94-250, CNES, France (1994)Google Scholar
  14. 14.
    San Juan, J.F.: Manipulación algebraica de series de Poisson. Aplicación a la teoría del satélite artificial. Ph. D. Dissertation, Univ. of Zaragoza (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • J. F. San Juan
    • 1
  • S. Serrano
    • 2
  • A. Abad
    • 2
  1. 1.Universidad de La RiojaLogroño
  2. 2.Universidad de ZaragozaZaragozaSpain

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