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Bestiary t0(2,66)

From Rose (2016)

Bestiary t0(2,66) is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 36.94 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 43.78), so a small nudge makes it unravel over a few periods. The bodies pass within 0.396 of each other at a top speed of 1.66, line up 24 times a period, and the computed loop closes to 4.6×10⁻²⁹.

Measured over one period

Period: 36.94001257
Masses: 1 : 1 : 1
Energy: -1.00000
Angular momentum: 0
Closest approach: 0.3960
Top speed: 1.663
Path length: 83.759
Alignments per period: 24
Topology: (abAB)⁴ (free-group class)
Stability: unstable (|λ|max 43.78)
Loop closure: 4.6×10⁻²⁹

Neighbours on the map

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