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Choreography NC.7

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

Choreography NC.7 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 170.96 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 56545407), so a small nudge makes it unravel over a few periods. The bodies pass within 0.185 of each other at a top speed of 2.65, line up 48 times a period, and the computed loop closes to 2.3×10⁻²³.

Measured over one period

Period: 170.9644529
Masses: 1 : 1 : 1
Energy: -0.535118
Angular momentum: 0
Closest approach: 0.1851
Top speed: 2.646
Path length: 236.98
Alignments per period: 48
Stability: unstable (|λ|max 5.7×10⁸, published)
Loop closure: 2.3×10⁻²³

Neighbours on the map

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