Atlas178 of 3,942

Yarn VI.12.A

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

Yarn VI.12.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 112.84 time units, published by Šuvakov & Dmitrašinović (2013). Dense skeins of thread wound around a hollow core. It is unstable (largest Floquet multiplier 147.5), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000389 of each other at a top speed of 16, line up 96 times a period, and the computed loop closes to 9.5×10⁻²³.

Measured over one period

Period: 112.8382672
Masses: 1 : 1 : 1
Energy: -1.18354
Angular momentum: 0
Closest approach: 3.9×10⁻⁵
Top speed: 160.4
Path length: 261.20
Alignments per period: 96
Topology: (abaBAbabAB)⁶ (free-group class)
Stability: unstable (|λ|max 147.5)
Loop closure: 9.5×10⁻²³

Neighbours on the map

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