Atlas77 of 3,915

Yin-Yang III.9.Aβ

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

Yin-Yang III.9.Aβ is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 32.841 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 0.0015 of each other at a top speed of 25.8, line up 60 times a period, and the computed loop closes to 7.7×10⁻²⁶.

Measured over one period

Period: 32.84083605
Masses: 1 : 1 : 1
Energy: -1.94098
Angular momentum: 0
Closest approach: 0.001504
Top speed: 25.84
Path length: 93.767
Alignments per period: 60
Stability: weakly unstable (|λ|max 9.939)
Loop closure: 7.7×10⁻²⁶

Neighbours on the map

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