New Stacked Central Configurations for the Spatial Seven-Body Problem

Abstract

In this paper we show the existence of three new families of spatial central configurations for the 7-body problem. More precisely, the position vectors x 1 , x 2 , x 3 , x 4 and x 5 are at the vertices of a square pyramid, the position vectors x 6 and x 7 are on a line connecting x 5 with the center of the opposite square.