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Choreography NC.28

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

Choreography NC.28 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 110.68 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 27116104), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00286 of each other at a top speed of 18.9, line up 72 times a period, and the computed loop closes to 5.5×10⁻²³.

Measured over one period

Period: 110.6813638
Masses: 1 : 1 : 1
Energy: -0.978358
Angular momentum: 0
Closest approach: 0.002861
Top speed: 18.93
Path length: 212.26
Alignments per period: 72
Topology: aabABabABabAABabAbABabABabABaBabABBabABabABabbAB (free-group class)
Stability: unstable (|λ|max 2.7×10⁷, published)
Loop closure: 5.5×10⁻²³

Neighbours on the map

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