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Choreography NC.137

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

Choreography NC.137 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 221.69 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 10990407735), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00258 of each other at a top speed of 19.7, line up 240 times a period, and the computed loop closes to 1.6×10⁻²⁰.

Measured over one period

Period: 221.6857450
Masses: 1 : 1 : 1
Energy: -1.40386
Angular momentum: 0
Closest approach: 0.002580
Top speed: 19.71
Path length: 590.61
Alignments per period: 240
Stability: unstable (|λ|max 1.1×10¹⁰, published)
Loop closure: 1.6×10⁻²⁰

Neighbours on the map

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