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Choreography NC.27

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

Choreography NC.27 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 97.624 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 1644600715), so a small nudge makes it unravel over a few periods. The bodies pass within 0.115 of each other at a top speed of 3.25, line up 72 times a period, and the computed loop closes to 4.0×10⁻²³.

Measured over one period

Period: 97.62442317
Masses: 1 : 1 : 1
Energy: -1.06243
Angular momentum: 0
Closest approach: 0.1150
Top speed: 3.253
Path length: 200.50
Alignments per period: 72
Topology: aabAAbaBAbABaBabABBabaBAbabAABabAbABaBAbaBBabbAB (free-group class)
Stability: unstable (|λ|max 1.6×10⁹, published)
Loop closure: 4.0×10⁻²³

Neighbours on the map

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