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Choreography NC.75

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

Choreography NC.75 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 135.61 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 1094423), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000622 of each other at a top speed of 127, line up 132 times a period, and the computed loop closes to 1.8×10⁻¹⁹.

Measured over one period

Period: 135.6081573
Masses: 1 : 1 : 1
Energy: -1.30536
Angular momentum: 0
Closest approach: 6.2×10⁻⁵
Top speed: 126.9
Path length: 320.59
Alignments per period: 132
Topology: 0 (free-group class)
Stability: unstable (|λ|max 1.1×10⁶, published)
Loop closure: 1.8×10⁻¹⁹

Neighbours on the map

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