Existence of permanent capture regions in more realistic models

Establish whether permanent weak capture regions persist in more realistic dynamical models of the Solar System and the Milky Way’s gravitational perturbation beyond the simplified planar circular restricted three-body formulation that approximates the Galaxy by a point mass at the Galactic Center and assumes the Sun’s circular motion; specifically, determine if sets analogous to the infinite-cycle weak stability boundary enabling permanent capture by the Sun continue to exist under more detailed and higher-dimensional modeling assumptions.

Background

The paper studies permanent weak capture in a simplified planar circular restricted three-body framework with three point masses: a test particle P, the Sun S, and a point-mass PMW representing the Milky Way’s mass at the Galactic Center. Within this model, recent theoretical results (B24) show a fractal weak stability boundary W' that enables permanent weak capture.

The authors state that extending their analysis to more realistic models (e.g., full three-dimensional dynamics or more detailed Galactic tidal fields) is not undertaken here and explicitly conjecture that permanent capture regions would still exist under such extensions.