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Choreography NC.164

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

Choreography NC.164 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 262.13 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 53763947581), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00292 of each other at a top speed of 18.6, line up 330 times a period, and the computed loop closes to 2.7×10⁻²⁰.

Measured over one period

Period: 262.1285955
Masses: 1 : 1 : 1
Energy: -1.55149
Angular momentum: 0
Closest approach: 0.002921
Top speed: 18.57
Path length: 708.84
Alignments per period: 330
Stability: unstable (|λ|max 5.4×10¹⁰, published)
Loop closure: 2.7×10⁻²⁰

Neighbours on the map

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