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Choreography NC.133

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

Choreography NC.133 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 249.28 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 163137), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0195 of each other at a top speed of 7.18, line up 240 times a period, and the computed loop closes to 2.3×10⁻²⁵.

Measured over one period

Period: 249.2836827
Masses: 1 : 1 : 1
Energy: -1.29817
Angular momentum: 0
Closest approach: 0.01949
Top speed: 7.176
Path length: 639.89
Alignments per period: 240
Stability: unstable (|λ|max 1.6×10⁵, published)
Loop closure: 2.3×10⁻²⁵

Neighbours on the map

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