On the Stability of Planetary Motions During Stellar Approaches

The problem of the spatial motion of a passively gravitating body during an to the central body of a perturbing body – a test star – is considered. Using the exact expression of the force function, an integral invariant relationship – a quasi-integral – was found. Due to the quasi-integral, the regions of possible motion of the passively gravitating body, the surfaces of minimal energy (a generalization of the zero velocity surfaces), and the singular points of these surfaces were determined. The stability of planetary motion according to Hill during the approach of a test star to the Solar System was investigated. Criteria for the possibility, as well as the impossibility of capturing the passively gravitating body by the test star, were established. According to the Hill stability criteria, critical values of the orbital parameters of the test star were established, at which the planets of the Solar System either become satellites of the test star or leave the bounds of the Solar System.