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