2023/08/30 by Ivan Hristov, Radoslava Hristova, V. Dmitrašinović +2 · 3 voices · 2 citations
Engineering · Physics and Astronomy · #Astro and Planetary Science #Space Satellite Systems and Control #Spacecraft Dynamics and Control #astro-ph.EP #nlin.CD #physics.class-ph #physics.comp-ph
paper · pdf · doi:10.1007/s10569-023-10177-w
arxiv published 2023/08/30 · arxiv updated 2023/08/30 · openalex publication_date 2024/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23
Abstract Li and Liao announced (New Astron 70:22–26, 2019, arXiv:1805.07980v1 ) discovery of 313 periodic collisionless orbits’ initial conditions (i.c.s), 30 of which have equal masses, and 18 of these 30 orbits have physical periods (scale-invariant periods) T*lt;80 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>T</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:mo><</mml:mo> <mml:mn>80</mml:mn> </mml:mrow> </mml:math> . We revisited this work with the intention to improve both, its logical consistency and the numerical efficiency of the method. We have conducted a new search for periodic free-fall orbits, limited to the equal-mass case. Our search produced 24,582 i.c.s of equal-mass periodic orbits with scale-invariant period T*lt;80 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>T</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:mo><</mml:mo> <mml:mn>80</mml:mn> </mml:mrow> </mml:math> , corresponding to 12,409 distinct solutions, 236 of which are self-dual.