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Choreography NC.93

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

Choreography NC.93 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 131.48 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 216770890485601), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000133 of each other at a top speed of 86.6, line up 180 times a period, and the computed loop closes to 1.0×10⁻¹³.

Measured over one period

Period: 131.4840979
Masses: 1 : 1 : 1
Energy: -1.63807
Angular momentum: 0
Closest approach: 1.3×10⁻⁴
Top speed: 86.61
Path length: 350.94
Alignments per period: 180
Topology: 0 (free-group class)
Stability: unstable (|λ|max 2.2×10¹⁴, published)
Loop closure: 1.0×10⁻¹³

Neighbours on the map

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