Apologies if this is a bit general, even some pointers in the right direction would be great (reading material etc.)
Given an object of mass $m_3$ travelling outward at speed $v$ from the centre of mass of a binary star system of two stars of masses $m_1$ and $m_2$ at angle $\theta$ from the $m_1$ end of the major axis of the elliptical orbit of the binary system is there an inequality that determines if the body of mass $m_3$ will escape the binary system?
Many thanks in advance for any help.