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Choreography NC.69

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

Choreography NC.69 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 267.46 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 59737460954), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000685 of each other at a top speed of 38.4, line up 120 times a period, and the computed loop closes to 4.8×10⁻¹⁷.

Measured over one period

Period: 267.4588391
Masses: 1 : 1 : 1
Energy: -0.778765
Angular momentum: 0
Closest approach: 6.8×10⁻⁴
Top speed: 38.39
Path length: 493.53
Alignments per period: 120
Stability: unstable (|λ|max 6.0×10¹⁰, published)
Loop closure: 4.8×10⁻¹⁷

Neighbours on the map

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