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Choreography NC.79

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

Choreography NC.79 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 90.791 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 468907817017), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0343 of each other at a top speed of 5.66, line up 138 times a period, and the computed loop closes to 4.5×10⁻²¹.

Measured over one period

Period: 90.79061374
Masses: 1 : 1 : 1
Energy: -1.75240
Angular momentum: 0
Closest approach: 0.03434
Top speed: 5.664
Path length: 253.62
Alignments per period: 138
Topology: 0 (free-group class)
Stability: unstable (|λ|max 4.7×10¹¹, published)
Loop closure: 4.5×10⁻²¹

Neighbours on the map

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