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Choreography NC.91

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

Choreography NC.91 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 183.73 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 1804849280769691), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000257 of each other at a top speed of 197, line up 180 times a period, and the computed loop closes to 6.1×10⁻¹².

Measured over one period

Period: 183.7315575
Masses: 1 : 1 : 1
Energy: -1.30895
Angular momentum: 0
Closest approach: 2.6×10⁻⁵
Top speed: 197.4
Path length: 425.57
Alignments per period: 180
Stability: unstable (|λ|max 1.8×10¹⁵, published)
Loop closure: 6.1×10⁻¹²

Neighbours on the map

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