Atlas3,309 of 3,942

Choreography NC.109

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

Choreography NC.109 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 276.16 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 122226), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00026 of each other at a top speed of 62.1, line up 186 times a period, and the computed loop closes to 2.6×10⁻²².

Measured over one period

Period: 276.1556659
Masses: 1 : 1 : 1
Energy: -1.02268
Angular momentum: 0
Closest approach: 2.6×10⁻⁴
Top speed: 62.13
Path length: 609.27
Alignments per period: 186
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBabABabABabABAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbABabABabAB (free-group class)
Stability: unstable (|λ|max 1.2×10⁵, published)
Loop closure: 2.6×10⁻²²

Neighbours on the map

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