Atlas129 of 3,942

Butterfly IVb.17.A

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

Butterfly IVb.17.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 79.997 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 1.046), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00159 of each other at a top speed of 25.1, line up 128 times a period, and the computed loop closes to 5.3×10⁻²⁵.

Measured over one period

Period: 79.99723126
Masses: 1 : 1 : 1
Energy: -1.74376
Angular momentum: 0
Closest approach: 0.001592
Top speed: 25.06
Path length: 199.33
Alignments per period: 128
Topology: ababABAbabaBABababABABababABAbabaBABAbabaBABababABAbabaBABAbabaBABababABAB (free-group class)
Stability: weakly unstable (|λ|max 1.046)
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.