Atlas123 of 3,942

Butterfly IVb.9.A

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

Butterfly IVb.9.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 41.126 time units, published by Šuvakov & Dmitrašinović (2013). A second butterfly sequence with a different topology from class I. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.00239 of each other at a top speed of 20.4, line up 64 times a period, and the computed loop closes to 9.1×10⁻²⁶.

Measured over one period

Period: 41.12605536
Masses: 1 : 1 : 1
Energy: -1.73594
Angular momentum: 0
Closest approach: 0.002392
Top speed: 20.45
Path length: 109.32
Alignments per period: 64
Topology: ababABAbabABAbabABAbabaBABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 9.1×10⁻²⁶

Neighbours on the map

All Butterfly IVb orbits, the families of periodic three-body orbits, or the atlas map.