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Choreography NC.33

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

Choreography NC.33 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 31.057 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 240846811328471008), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0193 of each other at a top speed of 7.8, line up 78 times a period, and the computed loop closes to 2.1×10⁻¹⁵.

Measured over one period

Period: 31.05665709
Masses: 1 : 1 : 1
Energy: -2.33937
Angular momentum: 0
Closest approach: 0.01932
Top speed: 7.803
Path length: 93.517
Alignments per period: 78
Stability: unstable (|λ|max 2.4×10¹⁷, published)
Loop closure: 2.1×10⁻¹⁵

Neighbours on the map

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