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II.C.33

m₃ = 2

From Li & Liao (2017)

II.C.33 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 110.38 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 2.785), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000907 of each other at a top speed of 542, line up 196 times a period, and the computed loop closes to 4.2×10⁻²¹.

Measured over one period

Period: 110.3782010
Masses: 1 : 1 : 2
Energy: -3.00392
Angular momentum: 0
Closest approach: 9.1×10⁻⁶
Top speed: 542.3
Path length: 314.57
Alignments per period: 196
Topology: ababababABABABabababaBABABABabababABABABAbababaBABABABabababABABABAbababaBABABABabababABABABAbabababABABAB (free-group class)
Stability: weakly unstable (|λ|max 2.785)
Loop closure: 4.2×10⁻²¹

Neighbours on the map

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