Atlas1,960 of 3,942

II.C.114

m₃ = 0.5

From Li & Liao (2017)

II.C.114 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 119.22 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 3.683), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000131 of each other at a top speed of 101, line up 150 times a period, and the computed loop closes to 9.6×10⁻²⁴.

Measured over one period

Period: 119.2213003
Masses: 1 : 1 : 0.5
Energy: -0.979046
Angular momentum: 0
Closest approach: 1.3×10⁻⁴
Top speed: 101.1
Path length: 277.41
Alignments per period: 150
Topology: aaBAbaBAbaBAbaBAbabABabABabABabAAbaBAbaBAbaBAbaBABabABabABabABabAAbaBAbaBAbaBAbaBAbabABabABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 3.683)
Loop closure: 9.6×10⁻²⁴

Neighbours on the map

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