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Bestiary t0(8,6)

From Rose (2016)

Bestiary t0(8,6) is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 107.71 time units, published by Rose (2016). Orbits from Rose’s survey of the symmetry-reduced problem, which reaches parts of phase space the other searches do not. It is weakly unstable (largest Floquet multiplier 2.836), so a small nudge makes it unravel over a few periods. The bodies pass within 0.011 of each other at a top speed of 9.55, line up 72 times a period, and the computed loop closes to 3.0×10⁻²⁵.

Measured over one period

Period: 107.7138105
Masses: 1 : 1 : 1
Energy: -1.00000
Angular momentum: 0
Closest approach: 0.01096
Top speed: 9.550
Path length: 225.24
Alignments per period: 72
Topology: abaBAbabABAbabABabaBAB (free-group class, shape period T/2)
Stability: weakly unstable (|λ|max 2.836)
Loop closure: 3.0×10⁻²⁵

Neighbours on the map

All Rose’s Bestiary, the families of periodic three-body orbits, or the atlas map.