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II.C.20

m₃ = 2

From Li & Liao (2017)

II.C.20 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 66.456 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is linearly stable (largest Floquet multiplier 1.047), so a small nudge only makes it wobble. The bodies pass within 0.000186 of each other at a top speed of 12, line up 124 times a period, and the computed loop closes to 3.3×10⁻²⁴.

Measured over one period

Period: 66.45598600
Masses: 1 : 1 : 2
Energy: -3.12563
Angular momentum: 0
Closest approach: 1.9×10⁻⁴
Top speed: 119.7
Path length: 205.64
Alignments per period: 124
Topology: abababABABAbababaBABABabababABABABababaBABABAbababaBABABAbababABABAB (free-group class)
Stability: stable (|λ|max 1.047)
Loop closure: 3.3×10⁻²⁴

Neighbours on the map

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