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Choreography NC.67

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

Choreography NC.67 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 268.05 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 30576422), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000133 of each other at a top speed of 86.9, line up 120 times a period, and the computed loop closes to 3.0×10⁻¹⁸.

Measured over one period

Period: 268.0483542
Masses: 1 : 1 : 1
Energy: -0.777593
Angular momentum: 0
Closest approach: 1.3×10⁻⁴
Top speed: 86.88
Path length: 494.90
Alignments per period: 120
Topology: 0 (free-group class)
Stability: unstable (|λ|max 3.1×10⁷, published)
Loop closure: 3.0×10⁻¹⁸

Neighbours on the map

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