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Choreography NC.40

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

Choreography NC.40 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 187.88 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 144868607), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0744 of each other at a top speed of 3.9, line up 84 times a period, and the computed loop closes to 2.7×10⁻²⁴.

Measured over one period

Period: 187.8848108
Masses: 1 : 1 : 1
Energy: -0.749007
Angular momentum: 0
Closest approach: 0.07440
Top speed: 3.901
Path length: 328.44
Alignments per period: 84
Topology: (aabABaBabABBabAABabAbABabbAB)² (free-group class)
Stability: unstable (|λ|max 1.4×10⁸, published)
Loop closure: 2.7×10⁻²⁴

Neighbours on the map

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