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Bestiary t0(2,85)

From Rose (2016)

Bestiary t0(2,85) is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 129.3 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 unstable (largest Floquet multiplier 26.29), so a small nudge makes it unravel over a few periods. The bodies pass within 0.485 of each other at a top speed of 1.55, line up 84 times a period, and the computed loop closes to 5.1×10⁻²⁹.

Measured over one period

Period: 129.3000476
Masses: 1 : 1 : 1
Energy: -1.00000
Angular momentum: 0
Closest approach: 0.4851
Top speed: 1.553
Path length: 293.27
Alignments per period: 84
Topology: (abAB)⁷ (free-group class, shape period T/2)
Stability: unstable (|λ|max 26.29)
Loop closure: 5.1×10⁻²⁹

Neighbours on the map

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