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Choreography NC.64

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

Choreography NC.64 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 169.2 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 4423), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000546 of each other at a top speed of 42.8, line up 114 times a period, and the computed loop closes to 3.1×10⁻²³.

Measured over one period

Period: 169.2045732
Masses: 1 : 1 : 1
Energy: -1.02150
Angular momentum: 0
Closest approach: 5.5×10⁻⁴
Top speed: 42.84
Path length: 362.92
Alignments per period: 114
Topology: aaBAbaBAbaBAbaBabABabABabABAbaBAbaBAbaBABabABabABabAbaBAbaBAbaBAbbABabABabAB (free-group class)
Stability: unstable (|λ|max 4423, published)
Loop closure: 3.1×10⁻²³

Neighbours on the map

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