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II.C.81

m₃ = 2

From Li & Liao (2017)

II.C.81 m₃ = 2 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 2 that return to their starting positions and velocities every 167.7 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is weakly unstable (largest Floquet multiplier 3.330), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000233 of each other at a top speed of 338, line up 386 times a period, and the computed loop closes to 4.8×10⁻²².

Measured over one period

Period: 167.6967610
Masses: 1 : 1 : 2
Energy: -3.58229
Angular momentum: 0
Closest approach: 2.3×10⁻⁵
Top speed: 338.2
Path length: 540.39
Alignments per period: 386
Topology: abababaBABABAbababaBABABAbabababABABABabababABABABabababABABABabababABABABabababaBABABAbababaBABABAbabababABABABabababABABABabababABABABabababABABABAbababaBABABAbababaBABABABabababABABABabababABABABabababABABAB (free-group class)
Stability: weakly unstable (|λ|max 3.330)
Loop closure: 4.8×10⁻²²

Neighbours on the map

All II.C orbits, the families of periodic three-body orbits, or the atlas map.