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Butterfly IVb.20.A

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

Butterfly IVb.20.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 83.106 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 0.000289 of each other at a top speed of 58.8, line up 140 times a period, and the computed loop closes to 9.3×10⁻²⁵.

Measured over one period

Period: 83.10581041
Masses: 1 : 1 : 1
Energy: -1.81779
Angular momentum: 0
Closest approach: 2.9×10⁻⁴
Top speed: 58.83
Path length: 219.95
Alignments per period: 140
Topology: ababABAbabaBABababABAbabABABabaBABAbabABAbabaBABababABAbabaBABabaBABAbabABABabaBAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 9.3×10⁻²⁵

Neighbours on the map

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