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II.C.30

m₃ = 2

From Li & Liao (2017)

II.C.30 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 97.179 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 1.064), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000114 of each other at a top speed of 484, line up 188 times a period, and the computed loop closes to 1.1×10⁻¹⁶.

Measured over one period

Period: 97.17915814
Masses: 1 : 1 : 2
Energy: -3.18585
Angular momentum: 0
Closest approach: 1.1×10⁻⁵
Top speed: 484.3
Path length: 291.43
Alignments per period: 188
Topology: abababaBABABAbabababABABABabababABABABabababaBABABAbabababABABABabababABABABAbababaBABABABabababABABAB (free-group class)
Stability: weakly unstable (|λ|max 1.064)
Loop closure: 1.1×10⁻¹⁶

Neighbours on the map

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