Atlas81 of 3,942

Yin-Yang III.13.Aβ

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

Yin-Yang III.13.Aβ is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 60.151 time units, published by Šuvakov & Dmitrašinović (2013). Two interlocking halves whose lobes wrap around each other. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.000611 of each other at a top speed of 40.4, line up 90 times a period, and the computed loop closes to 2.1×10⁻²⁵.

Measured over one period

Period: 60.15074367
Masses: 1 : 1 : 1
Energy: -1.69890
Angular momentum: 0
Closest approach: 6.1×10⁻⁴
Top speed: 40.44
Path length: 160.51
Alignments per period: 90
Topology: ababABAbabABAbabABAbabABAbabABabaBABabaBABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 2.1×10⁻²⁵

Neighbours on the map

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