Atlas2,164 of 3,915

II.C.188

m₃ = 0.5

From Li & Liao (2017)

II.C.188 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 140.25 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 3.591), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000000552 of each other at a top speed of 1555, line up 228 times a period, and the computed loop closes to 2.4×10⁻¹⁹.

Measured over one period

Period: 140.2477321
Masses: 1 : 1 : 0.5
Energy: -1.13842
Angular momentum: 0
Closest approach: 5.5×10⁻⁷
Top speed: 1555
Path length: 335.33
Alignments per period: 228
Stability: weakly unstable (|λ|max 3.591)
Loop closure: 2.4×10⁻¹⁹

Neighbours on the map

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