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Choreography NC.97

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

Choreography NC.97 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 223.93 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 20563228738), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000334 of each other at a top speed of 173, line up 186 times a period, and the computed loop closes to 1.8×10⁻¹⁵.

Measured over one period

Period: 223.9290363
Masses: 1 : 1 : 1
Energy: -1.17581
Angular momentum: 0
Closest approach: 3.3×10⁻⁵
Top speed: 173.0
Path length: 532.35
Alignments per period: 186
Stability: unstable (|λ|max 2.1×10¹⁰, published)
Loop closure: 1.8×10⁻¹⁵

Neighbours on the map

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