The asymptotic behavior of the secular perturbation function expanded in a power series in μ, the ratio of the semimajor axes of the massless point (asteroid) and Jupiter, is studied in the restricted spatial circular three-body problem. It is assumed that (internal case). A new derivation of the expansion of a secular perturbation function into a power series with coefficients expressed through Gauss and Clausen functions is described based on Parseval’s formula. For different values of μ at fixed values of the Lidov-Kozai constant, the radius of convergence of the reduced series, the areas of convergence and divergence are described in the plane of osculating elements e, ω. It is shown that power series is asymptotic in the sense of Poincaré in divergence regions, and that truncating the series after a 70 number of terms provides an high value approximation to a secular perturbation function. It is shown that the asymptotic properties of the series deteriorate on the nonanalyticity curves of secular perturbation function and completely disappear in a small neighborhood of . The asymptotic nature of the series allows, using ordinary methods of perturbation theory, to study the evolution of Keplerian orbital elements for all values of from the interval [0, 1), excluding the case .
On the Asymptotic Behavior of the Secular Perturbation Function in the Circular Restricted Three-Body Problem
Cosmic Res
Cosmic Research ; 62 , 3 ; 266-275
2024-06-01
10 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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