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Choreography NC.9

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

Choreography NC.9 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 143.78 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 1229657), so a small nudge makes it unravel over a few periods. The bodies pass within 0.184 of each other at a top speed of 2.51, line up 54 times a period, and the computed loop closes to 2.0×10⁻²⁴.

Measured over one period

Period: 143.7806466
Masses: 1 : 1 : 1
Energy: -0.642552
Angular momentum: 0
Closest approach: 0.1840
Top speed: 2.507
Path length: 230.01
Alignments per period: 54
Topology: aaabABaBaBabABBBabAAABabAbAbABabbbAB (free-group class)
Stability: unstable (|λ|max 1.2×10⁷, published)
Loop closure: 2.0×10⁻²⁴

Neighbours on the map

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