Atlas3,221 of 3,942

Choreography NC.124

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

Choreography NC.124 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 292.04 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 1650932136), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0631 of each other at a top speed of 4.08, line up 216 times a period, and the computed loop closes to 2.7×10⁻²⁴.

Measured over one period

Period: 292.0402152
Masses: 1 : 1 : 1
Energy: -1.08821
Angular momentum: 0
Closest approach: 0.06309
Top speed: 4.080
Path length: 662.61
Alignments per period: 216
Topology: aaBAbaBAbaBAbaBAbaBabABabABabABabABabABabABabABabAbaBAbaBAbaBAbaBAbbABabABabABabABabABabABabABabABAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 1.7×10⁹, published)
Loop closure: 2.7×10⁻²⁴

Neighbours on the map

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