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Bestiary t0(2,4)

From Rose (2016)

Bestiary t0(2,4) is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 193.64 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 0.0273 of each other at a top speed of 6.06, line up 128 times a period, and the computed loop closes to 1.6×10⁻²⁶.

Measured over one period

Period: 193.6448048
Masses: 1 : 1 : 1
Energy: -1.00000
Angular momentum: -3.8×10⁻⁶
Closest approach: 0.02730
Top speed: 6.057
Path length: 414.33
Alignments per period: 128
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: stable (|λ|max 1.000)
Loop closure: 1.6×10⁻²⁶

Neighbours on the map

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