Atlas2,147 of 3,942

II.C.220

m₃ = 0.5

From Li & Liao (2017)

II.C.220 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 170.34 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 3.969), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000529 of each other at a top speed of 159, line up 254 times a period, and the computed loop closes to 9.9×10⁻²⁴.

Measured over one period

Period: 170.3420494
Masses: 1 : 1 : 0.5
Energy: -1.08611
Angular momentum: 0
Closest approach: 5.3×10⁻⁵
Top speed: 158.7
Path length: 411.51
Alignments per period: 254
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabABabABabABabABabABabABabABabABabABabABabABabABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 3.969)
Loop closure: 9.9×10⁻²⁴

Neighbours on the map

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