Atlas2,196 of 3,942

II.C.48

m₃ = 0.5

From Li & Liao (2017)

II.C.48 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 60.798 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 3.186), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000152 of each other at a top speed of 296, line up 78 times a period, and the computed loop closes to 5.7×10⁻²³.

Measured over one period

Period: 60.79789694
Masses: 1 : 1 : 0.5
Energy: -0.980304
Angular momentum: 0
Closest approach: 1.5×10⁻⁵
Top speed: 295.9
Path length: 136.75
Alignments per period: 78
Topology: aabAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 3.186)
Loop closure: 5.7×10⁻²³

Neighbours on the map

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