Atlas3,257 of 3,942

Choreography NC.128

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

Choreography NC.128 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 178.4 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 195735), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000058 of each other at a top speed of 131, line up 228 times a period, and the computed loop closes to 6.9×10⁻²¹.

Measured over one period

Period: 178.3966488
Masses: 1 : 1 : 1
Energy: -1.56534
Angular momentum: 0
Closest approach: 5.8×10⁻⁵
Top speed: 131.4
Path length: 473.41
Alignments per period: 228
Topology: 0 (free-group class, shape period T/2)
Stability: unstable (|λ|max 2.0×10⁵, published)
Loop closure: 6.9×10⁻²¹

Neighbours on the map

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