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Choreography NC.89

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

Choreography NC.89 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 102.42 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 17973544376117), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000496 of each other at a top speed of 45, line up 168 times a period, and the computed loop closes to 2.6×10⁻¹⁷.

Measured over one period

Period: 102.4170043
Masses: 1 : 1 : 1
Energy: -1.85017
Angular momentum: 0
Closest approach: 5.0×10⁻⁴
Top speed: 45.00
Path length: 297.67
Alignments per period: 168
Topology: 0 (free-group class)
Stability: unstable (|λ|max 1.8×10¹³, published)
Loop closure: 2.6×10⁻¹⁷

Neighbours on the map

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