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<p>We show the existence of a new symmetric spatial central configuration for the 8-body problem: two rhombi rotated by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\pi /2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>π</mi> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月8日

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  • Antonio Carlos Fernandes,
  • Luis Fernando Mello

摘要

We show the existence of a new symmetric spatial central configuration for the 8-body problem: two rhombi rotated by \(\pi /2\) 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.