Critical orbits in the elliptic restricted three-body problem.

A numerical investigation of quasi-periodic orbits in the elliptic restricted three-body problem for different eccentricities of equally massive primaries is conducted to establish the regions of stable and unstable motions for some 2000 possible planetary orbits in double star systems. Results indicate an Upper Critical Orbit (UCO), outside of which all the orbits should be stable if they initially had only low eccentricity planet-like orbits, and a grey region of chaotic motion limited by the Lower Critical Orbit (LCO), within which all the integrated orbits were found to be unstable. A dependence of the distance of the LCO and UCO to the barycenter is established as a function of eccentricity of the primaries, and it is predicted that the region outside the UCO is the region of possible planetary motion in such double stars.