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Choreography NC.90

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

Choreography NC.90 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 106.54 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 906646852330176), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00443 of each other at a top speed of 15.1, line up 180 times a period, and the computed loop closes to 2.9×10⁻¹⁸.

Measured over one period

Period: 106.5410243
Masses: 1 : 1 : 1
Energy: -1.88060
Angular momentum: 0
Closest approach: 0.004433
Top speed: 15.09
Path length: 301.62
Alignments per period: 180
Stability: unstable (|λ|max 9.1×10¹⁴, published)
Loop closure: 2.9×10⁻¹⁸

Neighbours on the map

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