Atlas78 of 3,915

Yin-Yang III.16.Aβ

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

Yin-Yang III.16.Aβ is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 74.845 time units, published by Šuvakov & Dmitrašinović (2013). Two interlocking halves whose lobes wrap around each other. It is weakly unstable (largest Floquet multiplier 1.229), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00035 of each other at a top speed of 53.5, line up 110 times a period, and the computed loop closes to 7.4×10⁻²⁵.

Measured over one period

Period: 74.84521392
Masses: 1 : 1 : 1
Energy: -1.67878
Angular momentum: 0
Closest approach: 3.5×10⁻⁴
Top speed: 53.47
Path length: 198.68
Alignments per period: 110
Stability: weakly unstable (|λ|max 1.229)
Loop closure: 7.4×10⁻²⁵

Neighbours on the map

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