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Choreography NC.21

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

Choreography NC.21 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 140.7 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 0.0361 of each other at a top speed of 5.58, line up 66 times a period, and the computed loop closes to 3.0×10⁻²⁴.

Measured over one period

Period: 140.7010246
Masses: 1 : 1 : 1
Energy: -0.761204
Angular momentum: 0
Closest approach: 0.03609
Top speed: 5.577
Path length: 238.24
Alignments per period: 66
Topology: aaabABabAAABabAbAbABabABaBaBabABBBabABabbbAB (free-group class)
Stability: unstable (|λ|max 2.2×10⁷, published)
Loop closure: 3.0×10⁻²⁴

Neighbours on the map

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