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Choreography NC.38

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

Choreography NC.38 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 129.59 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 304962783019), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0306 of each other at a top speed of 5.75, line up 84 times a period, and the computed loop closes to 1.1×10⁻¹⁹.

Measured over one period

Period: 129.5944902
Masses: 1 : 1 : 1
Energy: -0.955535
Angular momentum: 0
Closest approach: 0.03060
Top speed: 5.754
Path length: 248.72
Alignments per period: 84
Topology: 0 (free-group class)
Stability: unstable (|λ|max 3.0×10¹¹, published)
Loop closure: 1.1×10⁻¹⁹

Neighbours on the map

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