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Choreography NC.56

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

Choreography NC.56 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 173.23 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 0.0175 of each other at a top speed of 7.78, line up 108 times a period, and the computed loop closes to 8.5×10⁻²⁰.

Measured over one period

Period: 173.2323292
Masses: 1 : 1 : 1
Energy: -0.968266
Angular momentum: 0
Closest approach: 0.01746
Top speed: 7.776
Path length: 353.70
Alignments per period: 108
Stability: unstable (|λ|max 1.3×10¹¹, published)
Loop closure: 8.5×10⁻²⁰

Neighbours on the map

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