Atlas118 of 3,942

Moth IVa.13.A

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

Moth IVa.13.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 90.035 time units, published by Šuvakov & Dmitrašinović (2013). Broad, fringed wings built from many overlapping passes. It is unstable (largest Floquet multiplier 384.8), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0169 of each other at a top speed of 7.7, line up 82 times a period, and the computed loop closes to 4.6×10⁻²⁸.

Measured over one period

Period: 90.03504380
Masses: 1 : 1 : 1
Energy: -1.25101
Angular momentum: 0
Closest approach: 0.01690
Top speed: 7.701
Path length: 227.12
Alignments per period: 82
Topology: abaBAbaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 384.8)
Loop closure: 4.6×10⁻²⁸

Neighbours on the map

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