On the spatial central configurations of the 5--body problem and their bifurcations

Abstract

Central configurations provide special solutions of the general $n$--body problem. Using the mutual distances between the $n$ bodies as coordinates we study the bifurcations of the spatial central configurations of the $5$--body problem going from the problem with equals masses to the $1+4$-- body problem which has one large mass and four infinitesimal equal masses. This study is made by giving a computer--aided proof.