Atlas2,200 of 3,942

II.C.233

m₃ = 0.5

From Li & Liao (2017)

II.C.233 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 170.43 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 4.710), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000293 of each other at a top speed of 67.5, line up 266 times a period, and the computed loop closes to 1.1×10⁻²⁴.

Measured over one period

Period: 170.4292590
Masses: 1 : 1 : 0.5
Energy: -1.11954
Angular momentum: 0
Closest approach: 2.9×10⁻⁴
Top speed: 67.46
Path length: 417.70
Alignments per period: 266
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabAbabABabABabABabABabABabABabABabABabABabABabABabABabABabABabABabABabAAbbAB (free-group class)
Stability: weakly unstable (|λ|max 4.710)
Loop closure: 1.1×10⁻²⁴

Neighbours on the map

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