I had a feeling once about Mathematics-that I saw it all. Depth beyond Depth was revealed to me-the Byss and the Abyss. I saw a quantity passing through infinity and changing its sign from plus to minus. I saw exactly how it happened and why the tergiversation was inevitable-but it was after dinner and I let it go.
Abstract
In a two body-problem, any type of variation in time of the Keplerian parameter μ (product of the constant of gravitationG by the reduced massm) causes a mean secular acceleration in the mean anomaly, but leaves the mean argument of perigee stationary. All asymptotic estimates for mean marginal rates of variation in the osculating elements, that Vinti established in the case whenG is inversely proportional to the time, are now extended to the most general kind of Gylden systems, and made into exact relations. The role of a Gylden system in explaining the marginal acceleration in the moon's mean motion is clarified. In addition, separable Gylden systems are classified from a physical standpoint by the integrals that they admit.
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Deprit, A. The secular acceleratons in Gylden's problem. Celestial Mechanics 31, 1–22 (1983). https://doi.org/10.1007/BF01272557
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DOI: https://doi.org/10.1007/BF01272557