Atlas44 of 3,942

Butterfly I.8.A

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

Butterfly I.8.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 34.247 time units, published by Šuvakov & Dmitrašinović (2013). Two wings of tight loops, with the bodies crossing through the centre at high speed. It is linearly stable (largest Floquet multiplier 1.014), so a small nudge only makes it wobble. The bodies pass within 0.00313 of each other at a top speed of 17.9, line up 54 times a period, and the computed loop closes to 5.7×10⁻²⁶.

Measured over one period

Period: 34.24704997
Masses: 1 : 1 : 1
Energy: -1.74960
Angular momentum: 0
Closest approach: 0.003132
Top speed: 17.87
Path length: 91.086
Alignments per period: 54
Topology: ababABAbabABAbabABABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.014)
Loop closure: 5.7×10⁻²⁶

Neighbours on the map

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