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Advances in Astronomy
Volume 2015, Article ID 649352, 11 pages
Research Article

Regions of Central Configurations in a Symmetric 4 + 1-Body Problem

Department of Mathematics, University of Ha’il, P.O. Box 2440, Ha’il 81451, Saudi Arabia

Received 30 September 2014; Revised 12 January 2015; Accepted 28 January 2015

Academic Editor: Dean Hines

Copyright © 2015 Muhammad Shoaib. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The inverse problem of central configuration of the trapezoidal 5-body problems is investigated. In this 5-body setup, one of the masses is chosen to be stationary at the center of mass of the system and four-point masses are placed on the vertices of an isosceles trapezoid with two equal masses at positions and at positions . The regions of central configurations where it is possible to choose positive masses are derived both analytically and numerically. It is also shown that in the complement of these regions no central configurations are possible.