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Choreography NC.48

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

Choreography NC.48 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 197.62 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 558457542999), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0116 of each other at a top speed of 9.56, line up 96 times a period, and the computed loop closes to 4.9×10⁻¹⁹.

Measured over one period

Period: 197.6237731
Masses: 1 : 1 : 1
Energy: -0.816482
Angular momentum: 0
Closest approach: 0.01158
Top speed: 9.559
Path length: 342.71
Alignments per period: 96
Stability: unstable (|λ|max 5.6×10¹², published)
Loop closure: 4.9×10⁻¹⁹

Neighbours on the map

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