Gyldén Model: The Slowly Changing Equivalent Gravitational Parameter
Authors: Cucu-Dumitrescu, C.; Selaru, D.
Source: Astrophysics and Space Science, Volume 250, Number 1, 1997 , pp. 93-107(15)
Abstract:In the Gyldén problem, the case of slowly changing equivalent gravitational parameter (e.g.p.) is studied. Assuming the following law for the variation of the e.g.p.: µ (t) = µ_0+ εµ (εt), ε≪ µ_0, we obtained a) a O(ε^4 T^4)-approximation of the solution, on a shortened time scale (0,T), with T of order o(ε^-1), for the general case (i.e. the support function µ is O(1)-valued and admits an expansion in power series of its argument), and b) a O(ε^2)-approximation of the solution, on a natural time scale of order O(1/ε), for the case of a bounded variation rate (i.e. the support function µ and its derivative are both O(1)-valued). For the study of the first problem we introduced a type of Lissajous variables and used the Lie-Hori normalization scheme; for the second problem we used the Delaunay variables and applied the von Zeipel method for approximate integration. The physical interpretation of the results is in both cases the same: within the corresponding limits of approximation, the variation of e.g.p. (i) has no effect on the size of the osculating ellipse, (ii) it sets the pericenter in slow rotation and (iii) it introduces a secular variation in the longitudes.
Document Type: Regular Paper
Affiliations: Institute for Gravitation and Space Sciences, 21-25 Mendeleev str., 70168 Bucharest, Romania
Publication date: 1997-01-01