Atlas133 of 3,942

Butterfly IVb.15.A

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

Butterfly IVb.15.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 68.066 time units, published by Šuvakov & Dmitrašinović (2013). A second butterfly sequence with a different topology from class I. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.00147 of each other at a top speed of 26.1, line up 104 times a period, and the computed loop closes to 5.3×10⁻²⁵.

Measured over one period

Period: 68.06563995
Masses: 1 : 1 : 1
Energy: -1.71807
Angular momentum: 0
Closest approach: 0.001469
Top speed: 26.09
Path length: 181.21
Alignments per period: 104
Topology: ababABAbabABAbabABAbabABAbabABAbabaBABabaBABabaBABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 5.3×10⁻²⁵

Neighbours on the map

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