  To apply Morse's critical point theory, we use mutual distances as
coordinates to discuss a kind of central configuration of the planar Newtonian
5-body problem with a trapezoidal convex hull, i.e., four of the five bodies
are located at the vertices of a trapezoid, and the fifth one is located on one
of the parallel sides. We show that there is at most one central configuration
of this geometrical shape for a given cyclic order of the five bodies along the
convex hull.
