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Choreography NC.30

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

Choreography NC.30 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 127.09 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 97333786), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0768 of each other at a top speed of 3.91, line up 72 times a period, and the computed loop closes to 1.9×10⁻²³.

Measured over one period

Period: 127.0919387
Masses: 1 : 1 : 1
Energy: -0.894124
Angular momentum: 0
Closest approach: 0.07679
Top speed: 3.913
Path length: 243.13
Alignments per period: 72
Topology: aabABabABabAABabAbABabABabABaBabABBabABabABabbAB (free-group class)
Stability: unstable (|λ|max 9.7×10⁷, published)
Loop closure: 1.9×10⁻²³

Neighbours on the map

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