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Choreography NC.101

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

Choreography NC.101 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 165.36 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 2737), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0227 of each other at a top speed of 6.71, line up 186 times a period, and the computed loop closes to 1.4×10⁻²⁵.

Measured over one period

Period: 165.3607720
Masses: 1 : 1 : 1
Energy: -1.43943
Angular momentum: 0
Closest approach: 0.02267
Top speed: 6.713
Path length: 437.80
Alignments per period: 186
Topology: aaBAbaBAbaBAbaBAbaBAbaBabABabABabABabABabABAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabAbaBAbaBAbaBAbaBAbaBAbbABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 27370, published)
Loop closure: 1.4×10⁻²⁵

Neighbours on the map

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