A formula for calculating higher-order perturbations in planetary problems

Details A formula for calculating higher-order perturbations in planetary problems A formula for calculating higher-order perturbations in planetary problems

May 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975cemec..11..379c&link_type=abstract

Celestial Mechanics, vol. 11, May 1975, p. 379-399. In French.

Computer Science

26

Fourier Series, Orbit Perturbation, Planetary Gravitation, Solar Orbits, Eccentric Orbits, Elliptical Orbits, Euler-Lagrange Equation, Iterative Solution, Perturbation Theory, Planetary Mass

Scientific paper

The authors present formulas in compact form for constructing high order planetary perturbations with respect to the disturbing masses. They have been built by an iterative process and give the variations of osculating elements. Singularities due to vanishing eccentricities and inclinations are not present in the differential equations. All elementary operations are manipulations of Fourier series with numerical coefficients, and great care has been taken to economize algebraic operations. Results are presented in three forms: (1) vectorial form, with real components which may be useful in numerical integrations; (2) complex form, to put in evidence the symmetries of the system of variables; (3) scalar form, which is the most elaborate. This last form has been used for constructing the first order perturbations for any pair of planets. Two illustrations are given (Jupiter and Saturn, Venus and Earth). Further remarks are made about the practical manipulation of Fourier series, resolution of Kepler's equation in complex form and construction by iteration of the inverse of the distance between two bodies.

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