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Choreography NC.1

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

Choreography NC.1 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 188.64 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 308567), so a small nudge makes it unravel over a few periods. The bodies pass within 0.441 of each other at a top speed of 1.86, line up 36 times a period, and the computed loop closes to 6.1×10⁻²⁶.

Measured over one period

Period: 188.6366241
Masses: 1 : 1 : 1
Energy: -0.429692
Angular momentum: 0
Closest approach: 0.4409
Top speed: 1.858
Path length: 253.61
Alignments per period: 36
Stability: unstable (|λ|max 3.1×10⁵, published)
Loop closure: 6.1×10⁻²⁶

Neighbours on the map

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