Abstract
The negative powers of the mutual distanceΔ −γ between two bodies are developed into series converging at any moment but that of collision. On the base of these expansions the series have been constructed representingΔ −γ in the perturbation theory of celestial mechanics. In the general case, including intersecting orbits, the terms are quasi-periodic functions of the time. In the case of non-intersecting orbits the expansion is a double Fourier series in the mean anomalies. All the expansions have a literal form with respect to osculating elements.
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References
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Petrovskaya, M.S. Expansions of the negative powers of mutual distances between bodies. Celestial Mechanics 3, 121–128 (1970). https://doi.org/10.1007/BF01230437
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DOI: https://doi.org/10.1007/BF01230437