Atlas2,204 of 3,942

II.C.125

m₃ = 0.5

From Li & Liao (2017)

II.C.125 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 132.01 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 1.677), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000164 of each other at a top speed of 90.1, line up 162 times a period, and the computed loop closes to 8.1×10⁻²⁵.

Measured over one period

Period: 132.0053085
Masses: 1 : 1 : 0.5
Energy: -0.951829
Angular momentum: 0
Closest approach: 1.6×10⁻⁴
Top speed: 90.10
Path length: 290.56
Alignments per period: 162
Topology: aabAbaBAbaBAbaBAbaBAbaBAbaBBaabAbbAABaBAbabAbaBAbaBAbaBAbaBAbbAAbaBBaabAbbAABaBAbaBAbaBAbaBAbaBAbaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 1.677)
Loop closure: 8.1×10⁻²⁵

Neighbours on the map

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