Atlas132 of 3,942

Butterfly IVb.15.Cα

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

Butterfly IVb.15.Cα is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 56.841 time units, published by Šuvakov & Dmitrašinović (2013). A second butterfly sequence with a different topology from class I. It is weakly unstable (largest Floquet multiplier 1.007), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000787 of each other at a top speed of 35.6, line up 106 times a period, and the computed loop closes to 3.9×10⁻²⁵.

Measured over one period

Period: 56.84080075
Masses: 1 : 1 : 1
Energy: -1.94383
Angular momentum: 0
Closest approach: 7.9×10⁻⁴
Top speed: 35.64
Path length: 154.99
Alignments per period: 106
Topology: ababABAbabaBABababABAbabaBABababABAbabABABabaBABAbabABABabaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.007)
Loop closure: 3.9×10⁻²⁵

Neighbours on the map

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