Bulirsh–Stoer algorithm in the planar restricted three-body problem

Abstract

The applicability of the Bulirsh–Stoer algorithm for solving the planar restricted three-body problem is investigated. Variations in the value of the Jacobi integral are considered as the main parameter. Massive calculations were carried out with a small step in the parameter characterizing the ratio of the masses of a planet and star (the mass parameter). It is shown that violations of the Jacobi integral occur inside the planetary chaotic region. This fact can be used to determine chaotic region boundaries, as well as the boundaries of a stable structure which coorbital with the planet. The average dependences of the value of the Jacobi integral on the mass parameter, which determine the boundaries of the chaotic zone and the coorbital ring, are derived. Estimates were obtained for the maximum relative change in the Jacobi integral for different values of the accretion radius. It is shown that the value of the accretion radius corresponding to the average radius of known exoplanets does not cause significant changes in the value of the Jacobi integral. The dependences of the clearing time of the chaotic zone for different accretion radii are also given with and without taking into account the coorbital structure.