Atlas35 of 3,942

Butterfly I.18.A

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

Butterfly I.18.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 76.029 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 1.000), so a small nudge only makes it wobble. The bodies pass within 0.000472 of each other at a top speed of 46, line up 122 times a period, and the computed loop closes to 4.3×10⁻²⁵.

Measured over one period

Period: 76.02852245
Masses: 1 : 1 : 1
Energy: -1.76663
Angular momentum: 0
Closest approach: 4.7×10⁻⁴
Top speed: 46.02
Path length: 201.62
Alignments per period: 122
Topology: ababABAbabABAbabaBABabaBABababABAbabABABabaBABabaBABAbabABAbabABABabaBAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 4.3×10⁻²⁵

Neighbours on the map

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