The secular accelerations in Gylden's problem

Details The secular accelerations in Gylden's problem The secular accelerations in Gylden's problem

Sep 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..31....1d&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 31, Sept. 1983, p. 1-22.

Mathematics

19

Acceleration (Physics), Celestial Mechanics, Moon, Secular Variations, Eccentricity, Time Dependence, Transformations (Mathematics)

Scientific paper

In a two body-problem, any type of variation in time of the Keplerian parameter μ (product of the constant of gravitation G by the reduced mass m) 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 when G 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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