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Choreography NC.76

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

Choreography NC.76 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 152.55 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 545028758), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00144 of each other at a top speed of 26.3, line up 132 times a period, and the computed loop closes to 8.0×10⁻²².

Measured over one period

Period: 152.5535196
Masses: 1 : 1 : 1
Energy: -1.20693
Angular momentum: 0
Closest approach: 0.001443
Top speed: 26.34
Path length: 349.76
Alignments per period: 132
Topology: 0 (free-group class)
Stability: unstable (|λ|max 5.5×10⁸, published)
Loop closure: 8.0×10⁻²²

Neighbours on the map

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