Atlas39 of 3,942

Butterfly I.20.A

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

Butterfly I.20.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 76.401 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 0.000201 of each other at a top speed of 70.6, line up 138 times a period, and the computed loop closes to 2.2×10⁻²⁴.

Measured over one period

Period: 76.40107866
Masses: 1 : 1 : 1
Energy: -1.89352
Angular momentum: 0
Closest approach: 2.0×10⁻⁴
Top speed: 70.56
Path length: 200.57
Alignments per period: 138
Topology: ababABAbabaBABababABABabaBABAbabaBABababABABabaBABAbabABABababABAbabaBABAbabABAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 2.2×10⁻²⁴

Neighbours on the map

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