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Choreography NC.15

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

Choreography NC.15 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 107.03 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 38348120217418), so a small nudge makes it unravel over a few periods. The bodies pass within 0.087 of each other at a top speed of 3.63, line up 60 times a period, and the computed loop closes to 9.3×10⁻¹⁹.

Measured over one period

Period: 107.0325092
Masses: 1 : 1 : 1
Energy: -0.898196
Angular momentum: 0
Closest approach: 0.08697
Top speed: 3.626
Path length: 199.15
Alignments per period: 60
Stability: unstable (|λ|max 3.8×10¹³, published)
Loop closure: 9.3×10⁻¹⁹

Neighbours on the map

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