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Choreography NC.114

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

Choreography NC.114 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 142.13 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 4116055111), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00716 of each other at a top speed of 11.9, line up 192 times a period, and the computed loop closes to 3.8×10⁻²².

Measured over one period

Period: 142.1342420
Masses: 1 : 1 : 1
Energy: -1.62503
Angular momentum: 0
Closest approach: 0.007159
Top speed: 11.93
Path length: 383.95
Alignments per period: 192
Stability: unstable (|λ|max 4.1×10⁹, published)
Loop closure: 3.8×10⁻²²

Neighbours on the map

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