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Choreography NC.52

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

Choreography NC.52 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 57.565 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 5196457832126), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0085 of each other at a top speed of 11.2, line up 108 times a period, and the computed loop closes to 3.8×10⁻¹⁹.

Measured over one period

Period: 57.56456797
Masses: 1 : 1 : 1
Energy: -1.92306
Angular momentum: 0
Closest approach: 0.008497
Top speed: 11.18
Path length: 159.80
Alignments per period: 108
Stability: unstable (|λ|max 5.2×10¹², published)
Loop closure: 3.8×10⁻¹⁹

Neighbours on the map

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