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Choreography NC.139

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

Choreography NC.139 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 241.61 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 30586516), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00717 of each other at a top speed of 11.8, line up 240 times a period, and the computed loop closes to 2.3×10⁻²⁶.

Measured over one period

Period: 241.6135095
Masses: 1 : 1 : 1
Energy: -1.32557
Angular momentum: 0
Closest approach: 0.007171
Top speed: 11.83
Path length: 626.07
Alignments per period: 240
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBabABabABabABabABabABAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 3.1×10⁷, published)
Loop closure: 2.3×10⁻²⁶

Neighbours on the map

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