Atlas88 of 3,942

Moth IVa.12.E

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

Moth IVa.12.E is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 83.984 time units, published by Šuvakov & Dmitrašinović (2013). Broad, fringed wings built from many overlapping passes. It is unstable (largest Floquet multiplier 12.37), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00833 of each other at a top speed of 10.9, line up 80 times a period, and the computed loop closes to 1.7×10⁻²⁵.

Measured over one period

Period: 83.98419376
Masses: 1 : 1 : 1
Energy: -1.27583
Angular momentum: 0
Closest approach: 0.008334
Top speed: 10.95
Path length: 202.23
Alignments per period: 80
Topology: abaBAbabABabaBAbabABabABAbaBABabaBAbabABAbaBABabAB (free-group class)
Stability: unstable (|λ|max 12.37)
Loop closure: 1.7×10⁻²⁵

Neighbours on the map

All Moth IVa orbits, the families of periodic three-body orbits, or the atlas map.