Atlas3,267 of 3,942

Choreography NC.147

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

Choreography NC.147 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 209.03 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 243046052), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00775 of each other at a top speed of 11.4, line up 258 times a period, and the computed loop closes to 2.8×10⁻²².

Measured over one period

Period: 209.0321301
Masses: 1 : 1 : 1
Energy: -1.53211
Angular momentum: 0
Closest approach: 0.007746
Top speed: 11.42
Path length: 573.84
Alignments per period: 258
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBabABabABabABabABabABAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 2.4×10⁸, published)
Loop closure: 2.8×10⁻²²

Neighbours on the map

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