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arXiv · 2602.17506

Scattering in the Positive Energy Isosceles Three-Body Problem

Richard Moeckel
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Abstract

In the three-body problem with positive energy, solutions which avoid triple collision have the property that the size of the triangle formed by the bodies tends to infinity as $t\rightarrow \pm\infty$. Furthermore, the triangles have well-defined asymptotic shapes $s_\pm$. The scattering problems asks which asymptotic shape $s_+$ can occur for a given choice of $s_-$. Previous work shows that this can be viewed as the problem of finding heteroclinic orbits connecting equilibrium points on a boundary manifold ``at infinity'' and some results were obtained for solutions which avoid collisions. The goal of this paper is to study the scattering effect of binary and near-triple collisions in a simple setting -- the isosceles three-body problem. The details depend on the mass parameters but in many cases, a fixed isosceles initial shape $s_-$ scatters to essentially all possible isosceles shapes $s_+$.

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Richard Moeckel. 2026-02-19. Scattering in the Positive Energy Isosceles Three-Body Problem. https://arxiv.org/abs/2602.17506

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