Central Configurations of an Isosceles Trapezoidal Five-Body Problem

Abstract

The study of central configurations is very popular for producing the simplest solutions of the planar n-body problems (cf., [1, 2, 4]). In this paper, we study the central configuration of the isosceles trapezoidal five-body problem where four of the masses are placed at the vertices of the isosceles trapezoid and the fifth body can take various positions on the axis of symmetry. We identify regions in the phase space where it is possible to choose positive masses which will make the configuration central. A similar approach was adopted by Shoaib et al. in [3] for the rhomboidal five-body problem.