Atlas32 of 3,942

Butterfly I.21.A

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

Butterfly I.21.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 76.593 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 0.000111 of each other at a top speed of 95, line up 146 times a period, and the computed loop closes to 3.4×10⁻²⁴.

Measured over one period

Period: 76.59274032
Masses: 1 : 1 : 1
Energy: -1.95395
Angular momentum: 0
Closest approach: 1.1×10⁻⁴
Top speed: 94.95
Path length: 198.50
Alignments per period: 146
Topology: ababABAbabaBABAbabaBABAbabaBABababABABababABABabaBABAbabaBABAbabaBABAbabABABababABAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 3.4×10⁻²⁴

Neighbours on the map

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