On constructions of spherical codes

Speaker: Ivan Hristov, FMI, Sofia University
Date: May 28, 2024
Time: 3:00 pm
Place: Room 503, IMI – BAS

Abstract: The classic gravitational three-body problem is considered. The motion of the bodies is determined by Newton’s second law and Newton’s law of universal gravitation. We are interested in a special case of planar periodic orbits – those that pass through Euler configuration.

In this talk a new efficient approach for searching three-body periodic equal-mass collisionless orbits passing through Euler configuration is presented [1]. The approach is based on a symmetry property of the solutions at the half period. Depending on two previously established symmetry types on the shape sphere, each solution is presented by one or two distinct initial conditions (one or two points in the search domain). A high precision numerical search based on Newton-Raphson method on a relatively coarse search grid for solutions with relatively short scale-invariant periods is conducted. The results of the search clearly demonstrate the efficiency of the approach. More than 12,000 initial conditions for periodic collisionless orbits (most of which new ones) are found. The extensive high precision computations are performed in Nestum cluster, Sofia Tech Park.

[1] Ivan Hristov, Radoslava Hristova. “An efficient approach for searching three-body periodic orbits passing through Eulerian configuration.” arXiv preprint arXiv:2404.16526 (2024).