Atlas3,278 of 3,942

Choreography NC.3

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

Choreography NC.3 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 106.14 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 1559883), so a small nudge makes it unravel over a few periods. The bodies pass within 0.222 of each other at a top speed of 2.41, line up 36 times a period, and the computed loop closes to 3.0×10⁻²⁶.

Measured over one period

Period: 106.1442429
Masses: 1 : 1 : 1
Energy: -0.631447
Angular momentum: 0
Closest approach: 0.2219
Top speed: 2.406
Path length: 164.06
Alignments per period: 36
Topology: aabAABabAbABaBabABBabbAB (free-group class)
Stability: unstable (|λ|max 1.6×10⁶, published)
Loop closure: 3.0×10⁻²⁶

Neighbours on the map

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