Atlas3,307 of 3,942

Choreography NC.155

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

Choreography NC.155 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 174.35 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 228847895559), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000458 of each other at a top speed of 148, line up 270 times a period, and the computed loop closes to 2.4×10⁻¹⁵.

Measured over one period

Period: 174.3532298
Masses: 1 : 1 : 1
Energy: -1.77995
Angular momentum: 0
Closest approach: 4.6×10⁻⁵
Top speed: 147.9
Path length: 496.18
Alignments per period: 270
Topology: 0 (free-group class)
Stability: unstable (|λ|max 2.3×10¹¹, published)
Loop closure: 2.4×10⁻¹⁵

Neighbours on the map

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