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Choreography NC.161

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

Choreography NC.161 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 297.64 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 13785312), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0223 of each other at a top speed of 6.7, line up 294 times a period, and the computed loop closes to 1.7×10⁻²².

Measured over one period

Period: 297.6411057
Masses: 1 : 1 : 1
Energy: -1.32093
Angular momentum: 0
Closest approach: 0.02231
Top speed: 6.704
Path length: 773.96
Alignments per period: 294
Stability: unstable (|λ|max 1.4×10⁷, published)
Loop closure: 1.7×10⁻²²

Neighbours on the map

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