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First-order theory of weakly eccentric orbital motion

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Abstract

Starting from the analytical theory of perturbed circular motions presented in “Celestial Mechanics” (Bois, 1994), this paper presents an extended resolution valid also for small eccentricity orbits. The solution is of the first order of a small parameter characterizing the magnitude of disturbing forces. The solution has the form of Fourier series with the coefficients given by iterative formation laws. The solution is free from singularities due to small eccentricity or inclination. As an example of numerical application the equatorial artificial satellite orbits are analyzed. For some high satellite orbits with small eccentricity the difference between the numerical integration and the analytical model does not exceed few centimeters per one revolution.

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Authors and Affiliations

  1. Dept. CERGA, Observatoire de la Côte d'Azur, Av. Copernic, F06130, Grasse, France

    Sławomir Breiter & Eric Bois

Authors
  1. Sławomir Breiter
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  2. Eric Bois
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On leave from Astronomical Observatory of A. Mickiewicz University, Słoneczna 36, PL60-286 Poznań, Poland.

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Breiter, S., Bois, E. First-order theory of weakly eccentric orbital motion. Celestial Mech Dyn Astr 60, 191–206 (1994). https://doi.org/10.1007/BF00693321

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  • DOI: https://doi.org/10.1007/BF00693321

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