Atlas29 of 3,942

Butterfly I.2.A

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

Butterfly I.2.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 6.2349 time units, published by Šuvakov & Dmitrašinović (2013). Two wings of tight loops, with the bodies crossing through the centre at high speed. It is weakly unstable (largest Floquet multiplier 1.776), so a small nudge makes it unravel over a few periods. The bodies pass within 0.011 of each other at a top speed of 9.55, line up 14 times a period, and the computed loop closes to 5.3×10⁻²⁸.

Measured over one period

Period: 6.234890472
Masses: 1 : 1 : 1
Energy: -2.17014
Angular momentum: 0
Closest approach: 0.01102
Top speed: 9.550
Path length: 16.783
Alignments per period: 14
Topology: ababABAB (free-group class)
Stability: weakly unstable (|λ|max 1.776)
Loop closure: 5.3×10⁻²⁸

Neighbours on the map

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