Atlas1,897 of 3,942

II.C.198

m₃ = 0.5

From Li & Liao (2017)

II.C.198 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 186.4 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 1.423), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000462 of each other at a top speed of 53.7, line up 230 times a period, and the computed loop closes to 3.8×10⁻²⁵.

Measured over one period

Period: 186.4022416
Masses: 1 : 1 : 0.5
Energy: -0.972166
Angular momentum: 0
Closest approach: 4.6×10⁻⁴
Top speed: 53.72
Path length: 436.09
Alignments per period: 230
Topology: aaBAbaBAbaBAbabABabABabAAbaBAbaBAbabABabABabAAbaBAbaBAbabABabABabAAbaBAbaBAbabABabABabAAbaBAbaBAbabABabABabAAbaBAbaBAbaBABabABabABaaBAbaBAbaBABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 1.423)
Loop closure: 3.8×10⁻²⁵

Neighbours on the map

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