Atlas30 of 3,942

Butterfly I.2.B

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

Butterfly I.2.B is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 7.0037 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 1.017), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0041 of each other at a top speed of 15.6, line up 14 times a period, and the computed loop closes to 4.7×10⁻²⁷.

Measured over one period

Period: 7.003698140
Masses: 1 : 1 : 1
Energy: -2.00820
Angular momentum: 0
Closest approach: 0.004099
Top speed: 15.62
Path length: 17.741
Alignments per period: 14
Topology: ababABAB (free-group class)
Stability: weakly unstable (|λ|max 1.017)
Loop closure: 4.7×10⁻²⁷

Neighbours on the map

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