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II.C.62

m₃ = 0.5

From Li & Liao (2017)

II.C.62 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 46.07 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 1.596), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000113 of each other at a top speed of 343, line up 94 times a period, and the computed loop closes to 5.0×10⁻¹⁷.

Measured over one period

Period: 46.06956316
Masses: 1 : 1 : 0.5
Energy: -1.32685
Angular momentum: 0
Closest approach: 1.1×10⁻⁵
Top speed: 342.8
Path length: 118.31
Alignments per period: 94
Topology: ababAbaBABaBAbabAbabABaBABabABabABabABabABAbABabaBabaBAbABAbaB (free-group class)
Stability: weakly unstable (|λ|max 1.596)
Loop closure: 5.0×10⁻¹⁷

Neighbours on the map

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