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Butterfly IVb.15.H

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

Butterfly IVb.15.H is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 78.868 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 1.233), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000523 of each other at a top speed of 43.8, line up 120 times a period, and the computed loop closes to 9.2×10⁻²⁵.

Measured over one period

Period: 78.86771190
Masses: 1 : 1 : 1
Energy: -1.69482
Angular momentum: 0
Closest approach: 5.2×10⁻⁴
Top speed: 43.75
Path length: 199.33
Alignments per period: 120
Topology: (ababABAbabaBAB)⁵ (free-group class)
Stability: weakly unstable (|λ|max 1.233)
Loop closure: 9.2×10⁻²⁵

Neighbours on the map

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