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Choreography NC.29

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

Choreography NC.29 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 120.78 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 512346034), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0594 of each other at a top speed of 4.37, line up 72 times a period, and the computed loop closes to 6.5×10⁻²⁴.

Measured over one period

Period: 120.7833829
Masses: 1 : 1 : 1
Energy: -0.923535
Angular momentum: 0
Closest approach: 0.05943
Top speed: 4.374
Path length: 230.20
Alignments per period: 72
Topology: aabABaBabAAbaBBabAbABabbABaBAbabABBabAABabaBAbAB (free-group class)
Stability: unstable (|λ|max 5.1×10⁸, published)
Loop closure: 6.5×10⁻²⁴

Neighbours on the map

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