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II.C.13

m₃ = 0.5

From Li & Liao (2017)

II.C.13 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 44.455 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 554.3), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00229 of each other at a top speed of 24.3, line up 26 times a period, and the computed loop closes to 1.6×10⁻²⁵.

Measured over one period

Period: 44.45457405
Masses: 1 : 1 : 0.5
Energy: -0.671676
Angular momentum: 0
Closest approach: 0.002286
Top speed: 24.32
Path length: 88.254
Alignments per period: 26
Stability: unstable (|λ|max 554.3)
Loop closure: 1.6×10⁻²⁵

Neighbours on the map

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