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Choreography NC.44

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

Choreography NC.44 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 194.46 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 18609221818977), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000743 of each other at a top speed of 367, line up 90 times a period, and the computed loop closes to 3.4×10⁻¹².

Measured over one period

Period: 194.4561654
Masses: 1 : 1 : 1
Energy: -0.794814
Angular momentum: 0
Closest approach: 7.4×10⁻⁶
Top speed: 367.2
Path length: 343.66
Alignments per period: 90
Stability: unstable (|λ|max 1.9×10¹³, published)
Loop closure: 3.4×10⁻¹²

Neighbours on the map

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