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Choreography NC.142

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

Choreography NC.142 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 241.35 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 154218533), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0172 of each other at a top speed of 7.65, line up 240 times a period, and the computed loop closes to 7.3×10⁻²².

Measured over one period

Period: 241.3512320
Masses: 1 : 1 : 1
Energy: -1.32655
Angular momentum: 0
Closest approach: 0.01718
Top speed: 7.646
Path length: 625.34
Alignments per period: 240
Stability: unstable (|λ|max 1.5×10⁸, published)
Loop closure: 7.3×10⁻²²

Neighbours on the map

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