Atlas3,218 of 3,942

Choreography NC.145

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

Choreography NC.145 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 206.12 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 615277647), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00199 of each other at a top speed of 22.5, line up 258 times a period, and the computed loop closes to 4.9×10⁻²¹.

Measured over one period

Period: 206.1199358
Masses: 1 : 1 : 1
Energy: -1.54642
Angular momentum: 0
Closest approach: 0.001986
Top speed: 22.52
Path length: 565.82
Alignments per period: 258
Topology: 0 (free-group class)
Stability: unstable (|λ|max 6.2×10⁸, published)
Loop closure: 4.9×10⁻²¹

Neighbours on the map

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