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Choreography NC.53

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

Choreography NC.53 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 242.81 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 33777436), so a small nudge makes it unravel over a few periods. The bodies pass within 0.06 of each other at a top speed of 4.26, line up 102 times a period, and the computed loop closes to 1.6×10⁻²³.

Measured over one period

Period: 242.8083969
Masses: 1 : 1 : 1
Energy: -0.739248
Angular momentum: 0
Closest approach: 0.06001
Top speed: 4.263
Path length: 432.12
Alignments per period: 102
Topology: aaBAbaBAbABabaBAbaBABabAbaBAbaBBabAAbaBAbaBabABAbaBAbabABaBAbaBAbbAB (free-group class)
Stability: unstable (|λ|max 3.4×10⁷, published)
Loop closure: 1.6×10⁻²³

Neighbours on the map

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