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July 10, 2026Open Access

Bi-Rhomboidal Spatial Central Configuration for the Eight-Body Problem

AFAntônio Carlos FernandesUniversidade do Estado do Rio de Janeiro LMLuis Fernando Mello

Key Points

This work aims to identify a new symmetric spatial central configuration for the eight-body problem.
Analytical proofs are used to demonstrate the existence of the new configuration.
Numerical simulations are conducted to visualize the behavior of the proposed arrangement.
A new symmetric configuration of two rhombi in space was identified, with six bodies positioned in a specific plane and two others orthogonal to this plane.
Proofs for the results were shown to be simple and analytic.

Abstract

Abstract We show the existence of a new symmetric spatial central configuration for the 8-body problem: two rhombi rotated by /2 π / 2 relative to each other around a diagonal of one of the rhombi. More specifically: (i) six bodies are in a plane, four of which are collinear and symmetrically positioned with respect to the midpoint of the segment containing them, and two bodies are symmetrically positioned on a segment orthogonal to the previous one; (ii) the other two bodies are symmetrically positioned on a segment orthogonal to the plane containing the six previous bodies. The obtained results have simple and analytic proofs. Some numerical simulations are also presented.

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