Some Observaties on the Fig8 Solution of the 3BP

2017/07/07 by F. Janssens, Janssens, F. L.
Engineering · Physics and Astronomy · #Astro and Planetary Science #FOS: Mathematics #General Mathematics (math.GM) #Nuclear physics research studies #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.1707.06462

openalex publication_date 2017/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some properties of the periodic solution of the three-body problem where three particles of equal mass follow the same trajectory are discussed. This trajectory has the shape of a figure-8. The three particles have a constant separation in time of 1/3 of the period. The angular momentum of the system is zero. The paper by Broucke and Elipe1 gives a thorough overview of history of this solution and places this solution in the general framework of the periodic solutions of the three-body problem. The two most interesting properties are the triangular and collinear configuration. Their occurrence in well known quartic curves with a figure eight shape are collected as an appendix.

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