Abstract
In this paper we show the existence of new families of spatial central configurations for the 7-body problem. In the studied spatial central configurations, six bodies are at the vertices of two equilateral triangles , and one body is located out of the parallel distinct planes containing and . The results have simple and analytic proofs.
Highlights
In this paper we study spatial central configurations for the N-body problem
In Lehmann-Filhés (1891) and Wintner (1941) can be found classical examples of spatial central configurations where the bodies with suitable masses are at the vertices of a regular tetrahedron and a regular octahedron, respectively
If we remove the body of mass m7 the remaining six bodies are already in a central configuration
Summary
In this paper we study spatial central configurations for the N-body problem. To know the central configurations for a given set of bodies with positive masses is a very hard and unsolved problem even in the case of few bodies.
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