New spatial central configurations in the 5-body problem

Luis Fernando Mello ,Antônio Carlos Fernandes

doi:10.1590/s0001-37652011005000023

Luis Fernando Mello , Antônio Carlos Fernandes

Open Access

https://doi.org/10.1590/s0001-37652011005000023

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Abstract

In this paper we show the existence of new families of convex and concave spatial central configurations for the 5-body problem. The bodies studied here are arranged as follows: three bodies are at the vertices of an equilateral triangle T, and the other two bodies are on the line passing through the barycenter of T that is perpendicular to the plane that contains T.

Highlights

Consider n punctual positive masses m1, . . . , mn with position vectors r1, . . . , rn
The Newtonian n-body problem in celestial mechanics consists in studying the motion of theses masses interacting amongst themselves through no other forces than their mutual gravitational attraction according to Newton’s gravitational law (Newton 1687)
In this paper we study spatial central configurations for the 5-body problem that satisfy (see Fig. 1(a) and 1(b)): 1. The position vectors r1, r2 and r3 are at the vertices of an equilateral triangle T ; 2

Summary

Introduction

Consider n punctual positive masses m1, . . . , mn with position vectors r1, . . . , rn. The same authors studied central configurations of three regular polyhedra for the spatial 3n-body problem in (Corbera and Llibre 2009).

Results

Conclusion