2016MNRAS.462..429G

We consider motion of a passive-gravitating body when a test star (perturbing body) approaches the central body. An integral invariant relation - a quasi-integral - is found by using exact expression of the force function, and regions of possible motion of a passive-gravitating body are determined. The surfaces of minimal energy (a generalization of zero velocity surfaces) are plotted, singular points of these surfaces are determined, their type and Lyapunov stability are established. Hill's stability of planetary motion is investigated for the case of a test star approaching the Solar system. Criteria for capture of a passive-gravitating body by a test star being possible and impossible are derived. Based on Hill stability criteria, we find critical parameters of the test star's orbit that leave planets bound to the Solar system.