Atlas3,201 of 3,942

Choreography NC.131

From Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2024)

Choreography NC.131 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 226.56 time units, published by Hristov, Hristova, Puzynin, Puzynina, Sharipov & Tukhliev (2024). Choreographies whose knot is not a power of the figure-eight’s: three bodies on one closed curve with a topology of its own. Computed to 180 digits; all unstable. It is unstable (largest Floquet multiplier 752938660994), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00121 of each other at a top speed of 28.8, line up 240 times a period, and the computed loop closes to 2.6×10⁻¹⁸.

Measured over one period

Period: 226.5579460
Masses: 1 : 1 : 1
Energy: -1.38359
Angular momentum: 0
Closest approach: 0.001208
Top speed: 28.78
Path length: 599.23
Alignments per period: 240
Topology: 0 (free-group class)
Stability: unstable (|λ|max 7.5×10¹¹, published)
Loop closure: 2.6×10⁻¹⁸

Neighbours on the map

All Nontrivial choreographies, the families of periodic three-body orbits, or the atlas map.