Satellite capture in a four-body system

Satellite capture is analyzed under the scope of a four-body system consisting of the central body S, the primary body X, and two minor bodies G and s. Should G and s form a binary system, capture of one of the bodies in the binary by the primary planet X is most conveniently analyzed in planetocentric representation of X. Satellite capture is dynamically possible even if the relative energy of the incoming binary with respect to the interacting primary body is significantly large.