Atlas75 of 3,915

Yin-Yang III.19.Aβ

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

Yin-Yang III.19.Aβ is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 86.402 time units, published by Šuvakov & Dmitrašinović (2013). Two interlocking halves whose lobes wrap around each other. It is weakly unstable (largest Floquet multiplier 6.018), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000568 of each other at a top speed of 42, line up 130 times a period, and the computed loop closes to 4.6×10⁻²⁰.

Measured over one period

Period: 86.40199179
Masses: 1 : 1 : 1
Energy: -1.70527
Angular momentum: 0
Closest approach: 5.7×10⁻⁴
Top speed: 41.96
Path length: 231.23
Alignments per period: 130
Stability: weakly unstable (|λ|max 6.018)
Loop closure: 4.6×10⁻²⁰

Neighbours on the map

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