Orbital evolution of the outer satellites of giant planets. Methods of analysis and results

The methods and results of analysis of the orbital evolution of outer satellites of giant planets are presented. The substantial irregularity of their orbits required the refinement of the already known and the development of new analytical methods for analyzing their long-term evolution. These methods are based on various averaged variants of the Hill problem. H.Kinoshita, H.Nakai, and the author of this paper further extended the qualitative analyses of these variants earlier performed by N. D. Moiseev, A. A. Orlov, M. L. Lidov, and Y.Kozai, by constructing the general solution of the double averaged Hill problem and by developing a combined numerical-analytical method. In this paper we present the results graphical form (time dependences of the orbital elements) obtained by various methods. We compare these results with those obtained by the most accurate method to numerically integrate the equations of perturbed motion of real satellites of giant planets. We put special emphasis on the satellite orbits with librational behavior of the variation of the pericenter argument. This libration is usually associated with the well-known Lidov-Kozai resonance, however, in the case of orbits of three Jovian satellites it is determined by large-amplitude periodic solar perturbations. The research, that we present here, stemmed from our interest in new distant satellites of giant planets and, in particular, in the celestial-mechanical effects that show up in the orbital evolution of these peculiar celestial objects.