Atlas2,046 of 3,942

II.C.16

m₃ = 0.5

From Li & Liao (2017)

II.C.16 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 22.513 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 8.220), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00243 of each other at a top speed of 23.3, line up 38 times a period, and the computed loop closes to 4.8×10⁻²⁶.

Measured over one period

Period: 22.51260572
Masses: 1 : 1 : 0.5
Energy: -1.19564
Angular momentum: 0
Closest approach: 0.002433
Top speed: 23.33
Path length: 56.702
Alignments per period: 38
Topology: aabAbbAABabAbabABabAAbbAB (free-group class)
Stability: weakly unstable (|λ|max 8.220)
Loop closure: 4.8×10⁻²⁶

Neighbours on the map

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