Atlas105 of 3,942

Moth IVa.13.C

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

Moth IVa.13.C is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 89.809 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 7.71, line up 82 times a period, and the computed loop closes to 2.1×10⁻²⁷.

Measured over one period

Period: 89.80897788
Masses: 1 : 1 : 1
Energy: -1.25311
Angular momentum: 0
Closest approach: 0.01687
Top speed: 7.707
Path length: 226.74
Alignments per period: 82
Topology: abaBAbaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 384.8)
Loop closure: 2.1×10⁻²⁷

Neighbours on the map

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