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Choreography NC.80

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

Choreography NC.80 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 98.779 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 112249700329), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00184 of each other at a top speed of 23.6, line up 138 times a period, and the computed loop closes to 1.1×10⁻¹⁹.

Measured over one period

Period: 98.77877949
Masses: 1 : 1 : 1
Energy: -1.65974
Angular momentum: 0
Closest approach: 0.001835
Top speed: 23.63
Path length: 267.57
Alignments per period: 138
Stability: unstable (|λ|max 1.1×10¹¹, published)
Loop closure: 1.1×10⁻¹⁹

Neighbours on the map

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