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arXiv · 2112.11922

Celestial Mechanics Solutions where the Future is a Perfect Reflection of the Past

Ali Abdulhussein·Harry Gingold
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Abstract

Newton's equations of celestial mechanics are shown to possess a continuum of solutions in which the future trajectories of the N bodies are a perfect reflection of their past. These solutions evolve from zero initial velocities of the N bodies. Consequently, the future gravitational forces acting on the N bodies are also a perfect reflection of their past. The proof is carried out via Taylor series expansions. A perturbed system of equations of the N body problem is also considered. All real valued solutions of this perturbed system have no singularities on the real line. The perturbed system is shown to have a continuum of solutions that possess symmetry where the future velocities of the N bodies are a perfect reflection of their past. The positions and accelerations of the N bodies are then odd functions of the time. All N bodies then evolve from one location in space.

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Ali Abdulhussein, Harry Gingold. 2021-12-20. Celestial Mechanics Solutions where the Future is a Perfect Reflection of the Past. https://arxiv.org/abs/2112.11922

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