Atlas67 of 3,942

Yin-Yang III.3.Aβ

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

Yin-Yang III.3.Aβ is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 10.963 time units, published by Šuvakov & Dmitrašinović (2013). Two interlocking halves whose lobes wrap around each other. It is weakly unstable (largest Floquet multiplier 1.905), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00979 of each other at a top speed of 10.2, line up 20 times a period, and the computed loop closes to 3.1×10⁻²⁸.

Measured over one period

Period: 10.96326982
Masses: 1 : 1 : 1
Energy: -1.93904
Angular momentum: 0
Closest approach: 0.009785
Top speed: 10.16
Path length: 31.322
Alignments per period: 20
Topology: ababABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.905)
Loop closure: 3.1×10⁻²⁸

Neighbours on the map

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