Atlas103 of 3,942

Moth IVa.8.F

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

Moth IVa.8.F is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 54.087 time units, published by Šuvakov & Dmitrašinović (2013). Broad, fringed wings built from many overlapping passes. It is weakly unstable (largest Floquet multiplier 6.808), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0147 of each other at a top speed of 8.26, line up 52 times a period, and the computed loop closes to 1.4×10⁻²⁵.

Measured over one period

Period: 54.08734180
Masses: 1 : 1 : 1
Energy: -1.29578
Angular momentum: 0
Closest approach: 0.01467
Top speed: 8.257
Path length: 137.24
Alignments per period: 52
Topology: abaBAbaBAbaBAbaBAbabABabABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 6.808)
Loop closure: 1.4×10⁻²⁵

Neighbours on the map

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