Atlas151 of 3,942

Butterfly IVb.23.D

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

Butterfly IVb.23.D is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 74.825 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 1.170), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000031 of each other at a top speed of 18, line up 164 times a period, and the computed loop closes to 1.3×10⁻²¹.

Measured over one period

Period: 74.82544684
Masses: 1 : 1 : 1
Energy: -2.13953
Angular momentum: 0
Closest approach: 3.1×10⁻⁵
Top speed: 179.8
Path length: 199.51
Alignments per period: 164
Topology: ababABAbabaBABAbabaBABAbabaBABAbabaBABababABABababABABababABABababABABababABABababABABababABAB (free-group class)
Stability: weakly unstable (|λ|max 1.170)
Loop closure: 1.3×10⁻²¹

Neighbours on the map

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