The stability of masses during three-body encounters

The dynamical interactio of a binary system and a third body not moving on a closed orbit arises in a large number of physical situations. The C²H condition for determining Hill stability of coplanar bound three-body systems is extended to cover situations where the outer body moves on a parabolic or hyperbolic orbit. Regions where such a body is stable against exchange or collision with other components of the system are determined for a number of important cases where closed solutions are possible.