Atlas3,227 of 3,942

Choreography NC.122

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

Choreography NC.122 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 235.33 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 94173543693), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000463 of each other at a top speed of 46.5, line up 204 times a period, and the computed loop closes to 3.3×10⁻¹⁷.

Measured over one period

Period: 235.3302520
Masses: 1 : 1 : 1
Energy: -1.21001
Angular momentum: 0
Closest approach: 4.6×10⁻⁴
Top speed: 46.50
Path length: 561.94
Alignments per period: 204
Topology: 0 (free-group class)
Stability: unstable (|λ|max 9.4×10¹⁰, published)
Loop closure: 3.3×10⁻¹⁷

Neighbours on the map

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