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arXiv · 2203.02793

Hundreds of new satellites of figure-eight orbit computed with high precision

I. Hristov·R. Hristova·I. Puzynin·T. Puzynina·Z. Sharipov·Z. Tukhliev
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Abstract

Satellites (topological powers) of the famous figure-eight orbit are special periodic solutions of the planar three-body problem. In this paper we use a modified Newton's method based on the Continuous analog of Newton's method and high precision arithmetic for a purposeful numerical search of new satellites of the figure-eight orbit. Over 700 new satellites are found, including 76 new linearly stable ones. 7 of the newly found linearly stable satellites are choreographies. The linear stability is checked by a high precision computing of the eigenvalues of the monodromy matrices. The initial conditions of all found solutions are given with 150 correct decimal digits.

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I. Hristov, R. Hristova, I. Puzynin, T. Puzynina, Z. Sharipov, Z. Tukhliev. 2022-03-05. Hundreds of new satellites of figure-eight orbit computed with high precision. https://doi.org/10.1063/5.0177835

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