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Choreography NC.57

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

Choreography NC.57 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 73.298 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 130315890919), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00984 of each other at a top speed of 10.4, line up 108 times a period, and the computed loop closes to 8.1×10⁻²⁰.

Measured over one period

Period: 73.29805118
Masses: 1 : 1 : 1
Energy: -1.71798
Angular momentum: 0
Closest approach: 0.009838
Top speed: 10.36
Path length: 199.35
Alignments per period: 108
Topology: 0 (free-group class)
Stability: unstable (|λ|max 1.3×10¹¹, published)
Loop closure: 8.1×10⁻²⁰

Neighbours on the map

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