Atlas3,245 of 3,942

Choreography NC.116

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

Choreography NC.116 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 251.44 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 81585), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000558 of each other at a top speed of 42.4, line up 192 times a period, and the computed loop closes to 2.3×10⁻²¹.

Measured over one period

Period: 251.4448858
Masses: 1 : 1 : 1
Energy: -1.11107
Angular momentum: 0
Closest approach: 5.6×10⁻⁴
Top speed: 42.39
Path length: 562.34
Alignments per period: 192
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBabABabABAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbABabAB (free-group class)
Stability: unstable (|λ|max 8.2×10⁵, published)
Loop closure: 2.3×10⁻²¹

Neighbours on the map

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