Atlas3,199 of 3,942

Choreography NC.160

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

Choreography NC.160 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 294.87 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 11765), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0114 of each other at a top speed of 9.37, line up 294 times a period, and the computed loop closes to 2.5×10⁻²⁵.

Measured over one period

Period: 294.8717570
Masses: 1 : 1 : 1
Energy: -1.32919
Angular momentum: 0
Closest approach: 0.01142
Top speed: 9.369
Path length: 769.13
Alignments per period: 294
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBabABabABabABabABabABabABabABabABAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabABabAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbABabABabABabABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 1.2×10⁵, published)
Loop closure: 2.5×10⁻²⁵

Neighbours on the map

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