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Bestiary t0(4,52)

From Rose (2016)

Bestiary t0(4,52) is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 79.274 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 21.76), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0258 of each other at a top speed of 6.23, line up 54 times a period, and the computed loop closes to 1.0×10⁻²⁷.

Measured over one period

Period: 79.27369560
Masses: 1 : 1 : 1
Energy: -0.999999
Angular momentum: 0
Closest approach: 0.02578
Top speed: 6.228
Path length: 159.12
Alignments per period: 54
Topology: ababABAbabABAbabABABabaBABabaBAB (free-group class)
Stability: unstable (|λ|max 21.76)
Loop closure: 1.0×10⁻²⁷

Neighbours on the map

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