Atlas31 of 3,942

Butterfly I.25.A

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

Butterfly I.25.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 90.562 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 0.0000703 of each other at a top speed of 119, line up 174 times a period, and the computed loop closes to 1.3×10⁻²³.

Measured over one period

Period: 90.56206322
Masses: 1 : 1 : 1
Energy: -1.96297
Angular momentum: 0
Closest approach: 7.0×10⁻⁵
Top speed: 119.2
Path length: 234.08
Alignments per period: 174
Topology: ababABAbabaBABAbabaBABAbabaBABababABABababABABababABABabaBABAbabaBABAbabaBABAbabABABababABABababABAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 1.3×10⁻²³

Neighbours on the map

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