Atlas1,844 of 3,915

II.C.106

m₃ = 0.5

From Li & Liao (2017)

II.C.106 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 69.217 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 2.954), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000051 of each other at a top speed of 162, line up 144 times a period, and the computed loop closes to 1.2×10⁻²³.

Measured over one period

Period: 69.21724224
Masses: 1 : 1 : 0.5
Energy: -1.35333
Angular momentum: 0
Closest approach: 5.1×10⁻⁵
Top speed: 161.7
Path length: 180.84
Alignments per period: 144
Stability: weakly unstable (|λ|max 2.954)
Loop closure: 1.2×10⁻²³

Neighbours on the map

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