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Choreography NC.34

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

Choreography NC.34 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 218.29 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 12670506473973), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00117 of each other at a top speed of 29.4, line up 78 times a period, and the computed loop closes to 8.1×10⁻¹⁷.

Measured over one period

Period: 218.2881564
Masses: 1 : 1 : 1
Energy: -0.664951
Angular momentum: 0
Closest approach: 0.001171
Top speed: 29.38
Path length: 353.28
Alignments per period: 78
Stability: unstable (|λ|max 1.3×10¹³, published)
Loop closure: 8.1×10⁻¹⁷

Neighbours on the map

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