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Choreography NC.12

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

Choreography NC.12 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 31.826 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 1676428), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0248 of each other at a top speed of 6.75, line up 54 times a period, and the computed loop closes to 1.7×10⁻²⁵.

Measured over one period

Period: 31.82589013
Masses: 1 : 1 : 1
Energy: -1.84950
Angular momentum: 0
Closest approach: 0.02482
Top speed: 6.755
Path length: 86.457
Alignments per period: 54
Stability: unstable (|λ|max 1.7×10⁶, published)
Loop closure: 1.7×10⁻²⁵

Neighbours on the map

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