Atlas82 of 3,942

Yin-Yang III.15.Aβ

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

Yin-Yang III.15.Aβ is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 66.751 time units, published by Šuvakov & Dmitrašinović (2013). Two interlocking halves whose lobes wrap around each other. It is weakly unstable (largest Floquet multiplier 1.001), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000742 of each other at a top speed of 36.7, line up 100 times a period, and the computed loop closes to 9.7×10⁻²⁵.

Measured over one period

Period: 66.75107838
Masses: 1 : 1 : 1
Energy: -1.70032
Angular momentum: 0
Closest approach: 7.4×10⁻⁴
Top speed: 36.72
Path length: 178.28
Alignments per period: 100
Topology: ababABAbabABAbabABAbabABAbabABAbaBABabaBABabaBABabaBABabaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.001)
Loop closure: 9.7×10⁻²⁵

Neighbours on the map

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