Basins of Escape of the Particle’s Planar Motion in the Rectilinear (3 $$\varvec{+}$$ 1)-Body Ring Problem

Abstract The objective of this work is to study the motion of an infinitesimal particle in the gravitational field of three big bodies in a ring configuration consisting of two peripheral and one central bodies, when the energy of the particle does not allow the escape from the potential well of the system. We have numerically determined the basins of escape using a new surface of section. Additionally, we have computed and analyzed the geometry of the set of asymptotic trajectories of the periodic orbit that governs the escape from the neighborhood of one of the two satellites, which also defines the limiting curves of the basins of escape from this region.