Atlas1,724 of 3,942

II.C.239

m₃ = 0.5

From Li & Liao (2017)

II.C.239 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 142.91 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 5.747), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000551 of each other at a top speed of 156, line up 276 times a period, and the computed loop closes to 4.0×10⁻²³.

Measured over one period

Period: 142.9115532
Masses: 1 : 1 : 0.5
Energy: -1.29608
Angular momentum: 0
Closest approach: 5.5×10⁻⁵
Top speed: 155.6
Path length: 369.47
Alignments per period: 276
Topology: aabAbaBABabAbabABaBABabAbaaBBabAAbbABaaBAbbAAbaBBaaBAbbAABaBAbabAbaBABabAbabABaBABabAbaaBBaBAAbbABaaBBabAAbbABaaBAbbAAbaBBaabAbaBABaBAbabAbaBABabAbabABaBAAbbABaaBBabAAbbABaaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 5.747)
Loop closure: 4.0×10⁻²³

Neighbours on the map

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