Atlas47 of 3,942

Butterfly I.9.A

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

Butterfly I.9.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 34.711 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 0.00107 of each other at a top speed of 30.6, line up 62 times a period, and the computed loop closes to 1.7×10⁻¹⁹.

Measured over one period

Period: 34.71149571
Masses: 1 : 1 : 1
Energy: -1.88117
Angular momentum: 0
Closest approach: 0.001068
Top speed: 30.61
Path length: 91.292
Alignments per period: 62
Topology: ababABAbabaBABababABABabaBABAbabABAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 1.7×10⁻¹⁹

Neighbours on the map

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