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II.C.23

m₃ = 0.5

From Li & Liao (2017)

II.C.23 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 22.957 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 20.81), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000126 of each other at a top speed of 103, line up 38 times a period, and the computed loop closes to 1.2×10⁻²³.

Measured over one period

Period: 22.95741389
Masses: 1 : 1 : 0.5
Energy: -1.28334
Angular momentum: 0
Closest approach: 1.3×10⁻⁴
Top speed: 102.9
Path length: 65.065
Alignments per period: 38
Topology: aaaaabAbbAAAAABabABabAB (free-group class)
Stability: unstable (|λ|max 20.81)
Loop closure: 1.2×10⁻²³

Neighbours on the map

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