Atlas33 of 3,942

Butterfly I.24.A

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

Butterfly I.24.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 90.356 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 0.000122 of each other at a top speed of 90.4, line up 166 times a period, and the computed loop closes to 5.0×10⁻²⁴.

Measured over one period

Period: 90.35628408
Masses: 1 : 1 : 1
Energy: -1.91238
Angular momentum: 0
Closest approach: 1.2×10⁻⁴
Top speed: 90.36
Path length: 236.43
Alignments per period: 166
Topology: ababABAbabaBABAbabaBABababABABabaBABAbabaBABababABABabaBABAbabaBABAbabABABababABAbabaBABAbabABAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 5.0×10⁻²⁴

Neighbours on the map

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