Abstract
The methods for an investigation of the evolution of orbits with large eccentricities are presented. The role of resonances in the motion of comets is considered. The expansion of the disturbing function in the restricted three-body problem is obtained for cometary orbits. The method is based on the proximity of cometary eccentricities to 1. The Hamiltonian describing the basic perturbations in the motion of long-period comets is constructed. It leads to mappings for the description of cometary dynamics.
The long-term evolution of short-period comets is considered. The importance of temporary librations near commensurabilities with Jupiter is emphasized. The analytical dependence of the diffusion rate upon the orbital elements of nearly-parabolic comets is found. The results of calculations of the diffusion rate taking into account perturbations from the outer planets are presented. A numerical study of cometary dynamics using mappings is carried out. A distribution like the Oort cloud is a typical stage of the evolution of comets in nearly-parabolic orbits under planetary perturbations.
A change of the partial density of meteor streams is studied. For the case of librations the dispersion speed of meteor streams under the action of planetary perturbations is substantially less than that for the case of typical chaos. A similarity between the observed structure of the meteor streams and resonant properties of the motion is discussed.
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