Numerical-Analytical Study of Linked Orbits in the Restricted Elliptic Doubly Averaged Three-Body Problem

Abstract

The restricted elliptic doubly averaged three-body problem is considered. The terms up to the second order inclusive with respect to the orbital eccentricity of the perturbing body are retained in the expansion of the perturbing function. The elements of the elliptical orbit for the perturbed body are deemed arbitrary. The special, so-called linked orbits of a negligible-mass body are investigated by numerically integrating the averaged equations in Keplerian elements. For such orbits the points of their intersection with the orbital plane of the perturbing body are on different sides of this orbit. The evolution of hypothetical and some real cometary orbits is described in the simplest Sun-Jupiter-comet model; their differences from the corresponding orbits in the circular problem have been revealed.