Abstract
A numerical-analytical method for analyzing the orbital evolution of a planetary satellite under the influence of a perturbing body moving in an elliptical orbit is described. In the averaged Gaussian scheme used this influence is replaced by the attraction of a material elliptical ring with the corresponding mass. Based on the closed analytical expression for the force function of such a ring derived by B.P. Kondrat’ev, we present formulas for the component of the attractive force acting on the planetary satellite. The method of numerical integration of the averaged equations in Keplerian elements is used to analyze the orbital evolution. We consider two methodological illustrative examples: Mercury as the main body, the Sun as the perturbing body, and an artificial Messenger-type satellite of Mercury; the Earth as the main body, the Moon and the Sun as the perturbing bodies, and a hypothetical artificial Earth satellite with its apogee outside the sphere with the radius of the lunar orbit. The described method can be used in evolution problems of celestial mechanics to study the perturbed motion of small Solar System bodies.
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ACKNOWLEDGMENTS
I am grateful to the two respected referees for their useful remarks on the paper and the revealed errors in its text.
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Translated by V. Astakhov
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Vashkov’yak, M.A. On the Attractive Force of an Elliptical Gaussian Ring. Sol Syst Res 55, 467–474 (2021). https://doi.org/10.1134/S0038094621050063
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DOI: https://doi.org/10.1134/S0038094621050063