Atlas1,969 of 3,942

II.C.127

m₃ = 0.5

From Li & Liao (2017)

II.C.127 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 117.33 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 746.6), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000429 of each other at a top speed of 55.7, line up 158 times a period, and the computed loop closes to 1.9×10⁻²⁴.

Measured over one period

Period: 117.3283821
Masses: 1 : 1 : 0.5
Energy: -1.03840
Angular momentum: 0
Closest approach: 4.3×10⁻⁴
Top speed: 55.71
Path length: 286.54
Alignments per period: 158
Topology: aaBAbaBAbabABabAAbaBAbabABabABaaBAbaBABabABaaBAbaBAbaBABabABaaBAbaBABabABabAAbaBAbabABabAAbaBAbaBABabAB (free-group class)
Stability: unstable (|λ|max 746.6)
Loop closure: 1.9×10⁻²⁴

Neighbours on the map

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