Atlas2,044 of 3,942

II.C.145

m₃ = 0.5

From Li & Liao (2017)

II.C.145 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 137.96 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 1.067), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000264 of each other at a top speed of 71.1, line up 184 times a period, and the computed loop closes to 5.1×10⁻²⁵.

Measured over one period

Period: 137.9566321
Masses: 1 : 1 : 0.5
Energy: -1.01246
Angular momentum: 0
Closest approach: 2.6×10⁻⁴
Top speed: 71.06
Path length: 323.75
Alignments per period: 184
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABabABabABabAAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 1.067)
Loop closure: 5.1×10⁻²⁵

Neighbours on the map

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