Atlas134 of 3,942

Butterfly IVb.22.A

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

Butterfly IVb.22.A is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 80.369 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 1.221), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00389 of each other at a top speed of 16.1, line up 152 times a period, and the computed loop closes to 8.2×10⁻²⁶.

Measured over one period

Period: 80.36874474
Masses: 1 : 1 : 1
Energy: -1.97439
Angular momentum: 0
Closest approach: 0.003894
Top speed: 16.05
Path length: 226.75
Alignments per period: 152
Topology: ababABAbabABAbabaBABabaBABabaBABAbabABAbabABAbabaBABabaBABababABAbabABAbabABABabaBABabaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.221)
Loop closure: 8.2×10⁻²⁶

Neighbours on the map

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