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Bestiary t0(8,4)

From Rose (2016)

Bestiary t0(8,4) is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 85.564 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 linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.0649 of each other at a top speed of 3.93, line up 56 times a period, and the computed loop closes to 1.1×10⁻²⁵.

Measured over one period

Period: 85.56418049
Masses: 1 : 1 : 1
Energy: -1.00000
Angular momentum: 0
Closest approach: 0.06491
Top speed: 3.934
Path length: 187.33
Alignments per period: 56
Topology: abaBAbaBAbabABabAB (free-group class, shape period T/2)
Stability: stable (|λ|max 1.000)
Loop closure: 1.1×10⁻²⁵

Neighbours on the map

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