Hundreds of new satellites of figure-eight orbit computed with high precision
Numerical Analysis
2023-11-27 v4 Earth and Planetary Astrophysics
Numerical Analysis
Chaotic Dynamics
Computational Physics
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.
Keywords
Cite
@article{arxiv.2203.02793,
title = {Hundreds of new satellites of figure-eight orbit computed with high precision},
author = {I. Hristov and R. Hristova and I. Puzynin and T. Puzynina and Z. Sharipov and Z. Tukhliev},
journal= {arXiv preprint arXiv:2203.02793},
year = {2023}
}
Comments
15 pages, 12 figures, 3 table