Three-body periodic collisionless equal-mass free-fall orbits revisited

Abstract

Li and Liao announced (2019) 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) $T^{\ast }=T|E{|}^{3/2}<80$. That work left a lot to be desired, however, both in terms of logical consistency and of numerical efficiency. 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 $T^{\ast }<80$, corresponding to 12,409 distinct solutions, 236 of which are self-dual.

arXiv comment21 pages, 15 figures, 3 tables

References in corpus (9)

• Three Classes of Newtonian Three-Body Planar Periodic Orbits
• More than six hundreds new families of Newtonian periodic planar collisionless three-body orbits
• Collisionless periodic orbits in the free-fall three-body problem
• From Brake to Syzygy
• Topological Dependence of Kepler's Third Law for Collisionless Periodic Three-Body Orbits with Vanishing Angular Momentum and Equal Masses
• Numerical Search for Periodic Solutions in the Vicinity of the Figure-Eight Orbit: Slaloming around Singularities on the Shape Sphere
• Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler's third law: a numerical test
• Mapping the three-body system - decay time and reversibility
• Periodic three-body orbits with vanishing angular momentum in the Jacobi-Poincare "strong" potential

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