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II.C.19

m₃ = 2

From Li & Liao (2017)

II.C.19 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 47.627 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 83.52), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000151 of each other at a top speed of 133, line up 122 times a period, and the computed loop closes to 8.4×10⁻²⁴.

Measured over one period

Period: 47.62651262
Masses: 1 : 1 : 2
Energy: -3.83616
Angular momentum: 0
Closest approach: 1.5×10⁻⁴
Top speed: 132.9
Path length: 153.59
Alignments per period: 122
Topology: ababababABABABabababaBABABAbabababABABABabababaBABABAbabababABABAB (free-group class)
Stability: unstable (|λ|max 83.52)
Loop closure: 8.4×10⁻²⁴

Neighbours on the map

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