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Yin-Yang III.18.Aβ

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

Yin-Yang III.18.Aβ is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 79.284 time units, published by Šuvakov & Dmitrašinović (2013). Two interlocking halves whose lobes wrap around each other. It is weakly unstable (largest Floquet multiplier 1.193), so a small nudge makes it unravel over a few periods. The bodies pass within 0.001 of each other at a top speed of 31.6, line up 120 times a period, and the computed loop closes to 3.7×10⁻²⁵.

Measured over one period

Period: 79.28350312
Masses: 1 : 1 : 1
Energy: -1.71202
Angular momentum: 0
Closest approach: 0.001004
Top speed: 31.56
Path length: 212.58
Alignments per period: 120
Stability: weakly unstable (|λ|max 1.193)
Loop closure: 3.7×10⁻²⁵

Neighbours on the map

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