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Choreography NC.20

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

Choreography NC.20 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 35.449 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 21712215), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0144 of each other at a top speed of 8.83, line up 66 times a period, and the computed loop closes to 6.7×10⁻²⁵.

Measured over one period

Period: 35.44882623
Masses: 1 : 1 : 1
Energy: -1.90823
Angular momentum: 0
Closest approach: 0.01440
Top speed: 8.830
Path length: 95.033
Alignments per period: 66
Topology: aaabABabAAABabAbAbABabABaBaBabABBBabABabbbAB (free-group class)
Stability: unstable (|λ|max 2.2×10⁷, published)
Loop closure: 6.7×10⁻²⁵

Neighbours on the map

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