Atlas3,284 of 3,942

Choreography NC.129

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

Choreography NC.129 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 165.33 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 954764812), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0214 of each other at a top speed of 6.96, line up 234 times a period, and the computed loop closes to 1.7×10⁻²¹.

Measured over one period

Period: 165.3349021
Masses: 1 : 1 : 1
Energy: -1.67697
Angular momentum: 0
Closest approach: 0.02136
Top speed: 6.955
Path length: 460.49
Alignments per period: 234
Topology: aaBAbaBAbaBAbaBabABabABabABabABabABabABabABabABabABabAbaBAbaBAbaBAbbABabABabABabABabABabABabABabABabABabABAbaBAbaBAbaBABabABabABabABabABabABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 9.5×10⁸, published)
Loop closure: 1.7×10⁻²¹

Neighbours on the map

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