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II.C.212

m₃ = 0.5

From Li & Liao (2017)

II.C.212 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 112.75 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 36.56), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000188 of each other at a top speed of 84.2, line up 246 times a period, and the computed loop closes to 6.4×10⁻²⁵.

Measured over one period

Period: 112.7541873
Masses: 1 : 1 : 0.5
Energy: -1.39758
Angular momentum: 0
Closest approach: 1.9×10⁻⁴
Top speed: 84.20
Path length: 294.14
Alignments per period: 246
Topology: aabAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbbAABaBBaabAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbbAABaBBaabAbaBAbbAABaBBaabAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbbAABaBBaabAbaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 36.56)
Loop closure: 6.4×10⁻²⁵

Neighbours on the map

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