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Choreography NC.6

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

Choreography NC.6 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 137.62 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 2065426556), so a small nudge makes it unravel over a few periods. The bodies pass within 0.212 of each other at a top speed of 2.7, line up 48 times a period, and the computed loop closes to 6.1×10⁻²³.

Measured over one period

Period: 137.6206990
Masses: 1 : 1 : 1
Energy: -0.617261
Angular momentum: 0
Closest approach: 0.2122
Top speed: 2.697
Path length: 218.52
Alignments per period: 48
Topology: aaabAAABabAbAbABaBaBabABBBabbbAB (free-group class)
Stability: unstable (|λ|max 2.1×10⁹, published)
Loop closure: 6.1×10⁻²³

Neighbours on the map

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