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Choreography NC.115

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

Choreography NC.115 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 263.49 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 113514632953), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000621 of each other at a top speed of 127, line up 192 times a period, and the computed loop closes to 2.7×10⁻¹⁷.

Measured over one period

Period: 263.4867920
Masses: 1 : 1 : 1
Energy: -1.07695
Angular momentum: 0
Closest approach: 6.2×10⁻⁵
Top speed: 127.0
Path length: 574.59
Alignments per period: 192
Stability: unstable (|λ|max 1.1×10¹¹, published)
Loop closure: 2.7×10⁻¹⁷

Neighbours on the map

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