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Choreography NC.72

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

Choreography NC.72 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 214.27 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 34728849046283932), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000253 of each other at a top speed of 63, line up 126 times a period, and the computed loop closes to 8.7×10⁻¹⁴.

Measured over one period

Period: 214.2650085
Masses: 1 : 1 : 1
Energy: -0.928854
Angular momentum: 0
Closest approach: 2.5×10⁻⁴
Top speed: 62.99
Path length: 411.38
Alignments per period: 126
Stability: unstable (|λ|max 3.5×10¹⁶, published)
Loop closure: 8.7×10⁻¹⁴

Neighbours on the map

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