Atlas36 of 3,942

Butterfly I.11.A

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

Butterfly I.11.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 47.925 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 1.002), so a small nudge only makes it wobble. The bodies pass within 0.00198 of each other at a top speed of 22.5, line up 74 times a period, and the computed loop closes to 4.1×10⁻²⁶.

Measured over one period

Period: 47.92549772
Masses: 1 : 1 : 1
Energy: -1.72805
Angular momentum: 0
Closest approach: 0.001980
Top speed: 22.48
Path length: 127.41
Alignments per period: 74
Topology: ababABAbabABAbabABAbabABABabaBABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.002)
Loop closure: 4.1×10⁻²⁶

Neighbours on the map

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