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II.C.13

m₃ = 2

From Li & Liao (2017)

II.C.13 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 39.635 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 2.845), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000538 of each other at a top speed of 223, line up 78 times a period, and the computed loop closes to 2.8×10⁻¹⁶.

Measured over one period

Period: 39.63529478
Masses: 1 : 1 : 2
Energy: -3.20865
Angular momentum: 0
Closest approach: 5.4×10⁻⁵
Top speed: 222.7
Path length: 112.58
Alignments per period: 78
Topology: ababababABABABAbabababABABABabababaBABABAB (free-group class)
Stability: weakly unstable (|λ|max 2.845)
Loop closure: 2.8×10⁻¹⁶

Neighbours on the map

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