Abstract
This paper consider the trapezoidal collinear four-body 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.
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