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Choreography NC.106

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

Choreography NC.106 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 150.75 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 105618358), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000057 of each other at a top speed of 133, line up 186 times a period, and the computed loop closes to 8.6×10⁻¹⁸.

Measured over one period

Period: 150.7514017
Masses: 1 : 1 : 1
Energy: -1.53107
Angular momentum: 0
Closest approach: 5.7×10⁻⁵
Top speed: 132.5
Path length: 408.29
Alignments per period: 186
Stability: unstable (|λ|max 1.1×10⁸, published)
Loop closure: 8.6×10⁻¹⁸

Neighbours on the map

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