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Choreography NC.130

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

Choreography NC.130 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 188.81 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 8253244938192), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0102 of each other at a top speed of 10, line up 240 times a period, and the computed loop closes to 1.8×10⁻¹⁷.

Measured over one period

Period: 188.8081896
Masses: 1 : 1 : 1
Energy: -1.56126
Angular momentum: 0
Closest approach: 0.01017
Top speed: 10.01
Path length: 501.33
Alignments per period: 240
Topology: 0 (free-group class)
Stability: unstable (|λ|max 8.3×10¹², published)
Loop closure: 1.8×10⁻¹⁷

Neighbours on the map

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