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This paper consider the trapezoidal collinear fourbody problem as a model for binary-binary gravitational interaction in star clusters. It has two degrees of freedom, it also is a sub-problem of the trapezoidal four-body problem that has three degrees of freedom. We prove that all its singularities in the trapezoidal four-body problem are due to collision and give some results regarding escapes to infinity. In order to give a description of the orbits suffering collisions between two bodies while the other two escape to infinity with zero radial velocity (parabolic orbits), we make use of the McGehee's techniques to blow-up-regularize the singularities due to collision and infinity.

In this paper, we consider the collinear symmetric four-body problem, where four masses m 3 = α, m 1 = 1, m 2 = 1, and m 4 = α, α > 0, are aligned in this order and move symmetrically about their center of mass. We introduce regularized variables to deal with binary collisions as well as McGehee coordinates to study the quadruple collision manifold for a negative value of the energy. The paper is mainly focused on orbits that eject from (or collide to) quadruple collision. The problem has two hyperbolic equilibrium points, located in the quadruple collision manifold. We use high order parametrizations of their stable/unstable manifolds to devise a numerical procedure to compute ejectioncollision orbits, for any value of α. Some results from the explorations done for α = 1 are presented. Furthermore, we prove the existence of ejection-direct escape orbits, which perform a unique type of binary collisions.

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