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Choreography NC.35

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

Choreography NC.35 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 201.67 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 2630461626998), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00944 of each other at a top speed of 10.6, line up 78 times a period, and the computed loop closes to 8.2×10⁻¹⁸.

Measured over one period

Period: 201.6716676
Masses: 1 : 1 : 1
Energy: -0.702528
Angular momentum: 0
Closest approach: 0.009444
Top speed: 10.57
Path length: 324.54
Alignments per period: 78
Topology: 0 (free-group class)
Stability: unstable (|λ|max 2.6×10¹², published)
Loop closure: 8.2×10⁻¹⁸

Neighbours on the map

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