| Abstract: |
| In order 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. In addition, if the parallel side containing the three collinear bodies is strictly shorter than the other parallel side, the configuration must be symmetric, i.e., the trapezoid is isosceles, and the last body is at the midpoint of the shorter parallel side. |
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