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.
Chapter PDF
Similar content being viewed by others
References
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)
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)
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)
Abad, A., San Juan, J.F., Gavín, A.: Short term evolution of artificial satellites. Celestial Mechanics and Dynamical Systems 79, 277–296 (2001)
Alfriend, K.T., Coffey, S.L.: Elimination of the Perigee in Satellite Problem. Celestial Mechanics 32, 163–172 (1984)
Bogoliubov, N.N., Mitropolsky, Y.A.: Asymptotic Method in the Theory of Nonlinear Oscillations. Gordon and Breach, New York (1961)
Deprit, A.: Canonical Transformations Depending on a Small Parameter. Celestial Mechanics 1, 12–30 (1969)
Deprit, A.: The Elimination of the Parallax in Satellite Theory. Celestial Mechanics 24, 111–153 (1981)
Desai, P.N., Braun, R.D., Powell, R.W.: Aspects of Parking Orbit Selection in a Manned Mars Mission, NASA TP-3256 (1992)
Henrard, J.: On a perturbation theory using Lie Transform. Celestial Mechanics 3, 107–120 (1970)
Kamel, A.A.: Perturbation methods in the theory of nonlinear oscillations. Celestial Mechanics 3, 90–106 (1970)
Krylov, N., Bogoliubov, N.N.: Introduction to Nonlinear Mechanics. Princeton University Press, Princeton (1947)
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)
San Juan, J.F.: Manipulación algebraica de series de Poisson. Aplicación a la teoría del satélite artificial. Ph. D. Dissertation, Univ. of Zaragoza (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Juan, J.F.S., Serrano, S., Abad, A. (2004). Analytical Theory of Motion of a Mars Orbiter. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science - ICCS 2004. ICCS 2004. Lecture Notes in Computer Science, vol 3039. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25944-2_42
Download citation
DOI: https://doi.org/10.1007/978-3-540-25944-2_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22129-6
Online ISBN: 978-3-540-25944-2
eBook Packages: Springer Book Archive