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

Abstract EN

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 m1=m4 at positions ∓0.5, rB and m2=m3 at positions ∓α/2,rA.

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.