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Choreography NC.159

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

Choreography NC.159 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 170.97 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 95402645421681136), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000156 of each other at a top speed of 253, line up 294 times a period, and the computed loop closes to 1.1×10⁻¹³.

Measured over one period

Period: 170.9672251
Masses: 1 : 1 : 1
Energy: -1.90471
Angular momentum: 0
Closest approach: 1.6×10⁻⁵
Top speed: 253.0
Path length: 489.31
Alignments per period: 294
Stability: unstable (|λ|max 9.5×10¹⁶, published)
Loop closure: 1.1×10⁻¹³

Neighbours on the map

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