Atlas176 of 3,942

Yarn VI.6.B

From Šuvakov & Dmitrašinović (2013). Sequences of orbits from the Belgrade three-body gallery.

Yarn VI.6.B is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 55.714 time units, published by Šuvakov & Dmitrašinović (2013). Dense skeins of thread wound around a hollow core. It is weakly unstable (largest Floquet multiplier 5.022), so a small nudge makes it unravel over a few periods. The bodies pass within 0.015 of each other at a top speed of 8.22, line up 48 times a period, and the computed loop closes to 2.1×10⁻²⁷.

Measured over one period

Period: 55.71413710
Masses: 1 : 1 : 1
Energy: -1.19350
Angular momentum: 0
Closest approach: 0.01499
Top speed: 8.222
Path length: 129.51
Alignments per period: 48
Topology: (abaBAbabAB)³ (free-group class)
Stability: weakly unstable (|λ|max 5.022)
Loop closure: 2.1×10⁻²⁷

Neighbours on the map

All Yarn VI orbits, the families of periodic three-body orbits, or the atlas map.