Atlas3,336 of 3,942

Choreography NC.31

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

Choreography NC.31 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 147.37 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 97333786), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0848 of each other at a top speed of 3.72, line up 72 times a period, and the computed loop closes to 2.5×10⁻²⁴.

Measured over one period

Period: 147.3706125
Masses: 1 : 1 : 1
Energy: -0.810094
Angular momentum: 0
Closest approach: 0.08476
Top speed: 3.724
Path length: 268.35
Alignments per period: 72
Topology: aabABabABabAABabAbABabABabABaBabABBabABabABabbAB (free-group class)
Stability: unstable (|λ|max 9.7×10⁷, published)
Loop closure: 2.5×10⁻²⁴

Neighbours on the map

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