Atlas3,226 of 3,942

Choreography NC.126

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

Choreography NC.126 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 258.43 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 165929384130109), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000557 of each other at a top speed of 42.4, line up 222 times a period, and the computed loop closes to 2.2×10⁻¹⁵.

Measured over one period

Period: 258.4273411
Masses: 1 : 1 : 1
Energy: -1.20260
Angular momentum: 0
Closest approach: 5.6×10⁻⁴
Top speed: 42.38
Path length: 608.60
Alignments per period: 222
Topology: 0 (free-group class)
Stability: unstable (|λ|max 1.7×10¹⁴, published)
Loop closure: 2.2×10⁻¹⁵

Neighbours on the map

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