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Choreography NC.13

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

Choreography NC.13 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 105.49 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 1676428), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0552 of each other at a top speed of 4.53, line up 54 times a period, and the computed loop closes to 9.9×10⁻²⁵.

Measured over one period

Period: 105.4889351
Masses: 1 : 1 : 1
Energy: -0.831961
Angular momentum: 0
Closest approach: 0.05517
Top speed: 4.531
Path length: 192.20
Alignments per period: 54
Topology: aabABabAABabAbABabABaBabABBabABabbAB (free-group class)
Stability: unstable (|λ|max 1.7×10⁶, published)
Loop closure: 9.9×10⁻²⁵

Neighbours on the map

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