Atlas3,288 of 3,942

Choreography NC.110

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

Choreography NC.110 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 196.08 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 652.6), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00951 of each other at a top speed of 10.3, line up 186 times a period, and the computed loop closes to 6.9×10⁻²⁵.

Measured over one period

Period: 196.0761233
Masses: 1 : 1 : 1
Energy: -1.28497
Angular momentum: 0
Closest approach: 0.009507
Top speed: 10.30
Path length: 486.44
Alignments per period: 186
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBabABabABabABAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbABabABabAB (free-group class)
Stability: unstable (|λ|max 652.6, published)
Loop closure: 6.9×10⁻²⁵

Neighbours on the map

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