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II.C.32

m₃ = 2

From Li & Liao (2017)

II.C.32 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 87.945 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 15.55), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000125 of each other at a top speed of 146, line up 194 times a period, and the computed loop closes to 1.1×10⁻²⁴.

Measured over one period

Period: 87.94472326
Masses: 1 : 1 : 2
Energy: -3.48924
Angular momentum: 0
Closest approach: 1.3×10⁻⁴
Top speed: 145.8
Path length: 284.41
Alignments per period: 194
Topology: abababABABAbababaBABABAbababaBABABAbababaBABABabababABABABabababABABABabababABABABabababABABABabababABABAB (free-group class)
Stability: unstable (|λ|max 15.55)
Loop closure: 1.1×10⁻²⁴

Neighbours on the map

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