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Choreography NC.149

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

Choreography NC.149 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 269.64 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 3378657), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0107 of each other at a top speed of 9.67, line up 258 times a period, and the computed loop closes to 1.6×10⁻²⁴.

Measured over one period

Period: 269.6438264
Masses: 1 : 1 : 1
Energy: -1.29298
Angular momentum: 0
Closest approach: 0.01070
Top speed: 9.666
Path length: 691.67
Alignments per period: 258
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBabABabABabABabABabABabABabABAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbABabABabABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 3.4×10⁶, published)
Loop closure: 1.6×10⁻²⁴

Neighbours on the map

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