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Choreography NC.85

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

Choreography NC.85 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 196.75 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 190940541011), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000416 of each other at a top speed of 49.3, line up 156 times a period, and the computed loop closes to 2.7×10⁻¹⁶.

Measured over one period

Period: 196.7533171
Masses: 1 : 1 : 1
Energy: -1.13752
Angular momentum: 0
Closest approach: 4.2×10⁻⁴
Top speed: 49.29
Path length: 440.47
Alignments per period: 156
Stability: unstable (|λ|max 1.9×10¹², published)
Loop closure: 2.7×10⁻¹⁶

Neighbours on the map

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