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II.C.240

m₃ = 0.5

From Li & Liao (2017)

II.C.240 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 142.25 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 9.969), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000242 of each other at a top speed of 235, line up 280 times a period, and the computed loop closes to 1.0×10⁻²².

Measured over one period

Period: 142.2515470
Masses: 1 : 1 : 0.5
Energy: -1.31811
Angular momentum: 0
Closest approach: 2.4×10⁻⁵
Top speed: 234.6
Path length: 372.46
Alignments per period: 280
Topology: aabAbaBABabAbaaBBabAAbbABaaBAbbAABaBAbabAbaBABabAbaaBBaBAAbbABaaBAbbAAbaBAbabAbaBABabAbaaBBaBAAbbABaaBAbbAAbaBBaabAbaBABabAbabABaBAAbbABaaBAbbAABaBAbabAbaBABabAbaaBBaBAAbbABaaBAbbAAbaBB (free-group class)
Stability: weakly unstable (|λ|max 9.969)
Loop closure: 1.0×10⁻²²

Neighbours on the map

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