Atlas72 of 3,942

Yin-Yang III.9.Aα

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

Yin-Yang III.9.Aα is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 50.407 time units, published by Šuvakov & Dmitrašinović (2013). Two interlocking halves whose lobes wrap around each other. It is weakly unstable (largest Floquet multiplier 9.939), so a small nudge makes it unravel over a few periods. The bodies pass within 0.002 of each other at a top speed of 22.4, line up 60 times a period, and the computed loop closes to 4.9×10⁻²⁶.

Measured over one period

Period: 50.40714638
Masses: 1 : 1 : 1
Energy: -1.45871
Angular momentum: 0
Closest approach: 0.002001
Top speed: 22.41
Path length: 124.77
Alignments per period: 60
Topology: (ababABAbaBAB)³ (free-group class)
Stability: weakly unstable (|λ|max 9.939)
Loop closure: 4.9×10⁻²⁶

Neighbours on the map

All Yin-Yang III orbits, the families of periodic three-body orbits, or the atlas map.