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Choreography NC.87

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

Choreography NC.87 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 169.53 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 580120171), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000108 of each other at a top speed of 304, line up 168 times a period, and the computed loop closes to 7.4×10⁻¹⁵.

Measured over one period

Period: 169.5317661
Masses: 1 : 1 : 1
Energy: -1.32077
Angular momentum: 0
Closest approach: 1.1×10⁻⁵
Top speed: 304.3
Path length: 394.74
Alignments per period: 168
Topology: 0 (free-group class)
Stability: unstable (|λ|max 5.8×10⁸, published)
Loop closure: 7.4×10⁻¹⁵

Neighbours on the map

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