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Choreography NC.65

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

Choreography NC.65 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 62.017 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 87668655624), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00785 of each other at a top speed of 12, line up 150 times a period, and the computed loop closes to 2.3×10⁻¹⁸.

Measured over one period

Period: 62.01725005
Masses: 1 : 1 : 1
Energy: -1.99908
Angular momentum: 0
Closest approach: 0.007852
Top speed: 11.97
Path length: 162.46
Alignments per period: 150
Stability: unstable (|λ|max 8.8×10¹⁰, published)
Loop closure: 2.3×10⁻¹⁸

Neighbours on the map

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