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Choreography NC.92

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

Choreography NC.92 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 109.43 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 38130457136173), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00014 of each other at a top speed of 84.5, line up 180 times a period, and the computed loop closes to 2.1×10⁻¹⁷.

Measured over one period

Period: 109.4296066
Masses: 1 : 1 : 1
Energy: -1.84976
Angular momentum: 0
Closest approach: 1.4×10⁻⁴
Top speed: 84.45
Path length: 308.35
Alignments per period: 180
Stability: unstable (|λ|max 3.8×10¹³, published)
Loop closure: 2.1×10⁻¹⁷

Neighbours on the map

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