Atlas2,155 of 3,942

II.C.131

m₃ = 0.5

From Li & Liao (2017)

II.C.131 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 116.33 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is weakly unstable (largest Floquet multiplier 1.291), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000429 of each other at a top speed of 176, line up 166 times a period, and the computed loop closes to 8.7×10⁻²⁴.

Measured over one period

Period: 116.3271633
Masses: 1 : 1 : 0.5
Energy: -1.04832
Angular momentum: 0
Closest approach: 4.3×10⁻⁵
Top speed: 176.3
Path length: 272.54
Alignments per period: 166
Topology: abaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABabABabABabABabABabABabABabABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 1.291)
Loop closure: 8.7×10⁻²⁴

Neighbours on the map

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