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Choreography NC.157

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

Choreography NC.157 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 180.85 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 71669102187146), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00015 of each other at a top speed of 81.9, line up 288 times a period, and the computed loop closes to 9.6×10⁻¹⁶.

Measured over one period

Period: 180.8519191
Masses: 1 : 1 : 1
Energy: -1.81340
Angular momentum: 0
Closest approach: 1.5×10⁻⁴
Top speed: 81.88
Path length: 513.52
Alignments per period: 288
Stability: unstable (|λ|max 7.2×10¹³, published)
Loop closure: 9.6×10⁻¹⁶

Neighbours on the map

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