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Choreography NC.50

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

Choreography NC.50 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 54.575 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 1646639977), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00835 of each other at a top speed of 11.6, line up 126 times a period, and the computed loop closes to 3.9×10⁻²¹.

Measured over one period

Period: 54.57537554
Masses: 1 : 1 : 1
Energy: -1.98763
Angular momentum: 0
Closest approach: 0.008354
Top speed: 11.60
Path length: 143.57
Alignments per period: 126
Stability: unstable (|λ|max 1.6×10¹⁰, published)
Loop closure: 3.9×10⁻²¹

Neighbours on the map

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