First-order theory of weakly eccentric orbital motion

Details First-order theory of weakly eccentric orbital motion First-order theory of weakly eccentric orbital motion

Oct 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..60..191b&link_type=abstract

Celestial Mechanics & Dynamical Astronomy (ISSN 0923-2958), vol. 60, no. 2, p. 191-206

Astronomy and Astrophysics

Astronomy

3

Celestial Mechanics, Eccentric Orbits, Equatorial Orbits, Kepler Laws, Orbit Perturbation, Satellite Orbits, Astronomical Models, Equations Of Motion, Numerical Integration, Perturbation Theory

Scientific paper

Starting from the analytical theory of perturbed circular motions presented in 'Celestial Mechanics', this paper presents an extended resolution valid 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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