Atlas3,228 of 3,942

Choreography NC.112

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

Choreography NC.112 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 152.89 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 15907924854), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00053 of each other at a top speed of 43.5, line up 186 times a period, and the computed loop closes to 1.4×10⁻¹⁷.

Measured over one period

Period: 152.8892269
Masses: 1 : 1 : 1
Energy: -1.51680
Angular momentum: 0
Closest approach: 5.3×10⁻⁴
Top speed: 43.45
Path length: 414.42
Alignments per period: 186
Topology: 0 (free-group class)
Stability: unstable (|λ|max 1.6×10¹⁰, published)
Loop closure: 1.4×10⁻¹⁷

Neighbours on the map

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