Atlas83 of 3,942

Yin-Yang III.15.Cβ

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

Yin-Yang III.15.Cβ is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 54.82 time units, published by Šuvakov & Dmitrašinović (2013). Two interlocking halves whose lobes wrap around each other. It is unstable (largest Floquet multiplier 26.65), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00514 of each other at a top speed of 14, line up 100 times a period, and the computed loop closes to 1.9×10⁻²⁶.

Measured over one period

Period: 54.82002201
Masses: 1 : 1 : 1
Energy: -1.93896
Angular momentum: 0
Closest approach: 0.005139
Top speed: 14.01
Path length: 156.57
Alignments per period: 100
Topology: (ababABAbaBAB)⁵ (free-group class)
Stability: unstable (|λ|max 26.65)
Loop closure: 1.9×10⁻²⁶

Neighbours on the map

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