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An interesting description of a collinear configuration of four particles isfound in terms of two spherical coordinates. An algorithm to compute the fourcoordinates of particles of a collinear Four-Body central configuration ispresented by using an orthocentric tetrahedron, which edge lengths are functionof given masses. Each mass is placed at the corresponding vertex of thetetrahedron. The center of mass (and orthocenter) of the tetrahedron is at theorigin of coordinates. The initial position of the tetrahedron is placed withtwo pairs of vertices each in a coordinate plan, the lines joining any pair ofthem parallel to a coordinate axis, the center of masses of each and the centerof mass of the four on one coordinate axis. From this original position thetetrahedron is rotated by two angles around the center of mass until thedirection of configuration coincides with one axis of coordinates. The fourcoordinates of the vertices of the tetrahedron along this direction determinethe central configuration by finding the two angles corresponding to it. Thetwelve possible configurations predicted by Moulton's theorem are computed fora particular mass choice.

Computing collinear 4-Body Problem central configurations with given masses