Atlas2,040 of 3,942

II.C.197

m₃ = 0.5

From Li & Liao (2017)

II.C.197 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 161.71 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 1.923), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000238 of each other at a top speed of 74.8, line up 230 times a period, and the computed loop closes to 1.5×10⁻²⁴.

Measured over one period

Period: 161.7072927
Masses: 1 : 1 : 0.5
Energy: -1.06876
Angular momentum: 0
Closest approach: 2.4×10⁻⁴
Top speed: 74.78
Path length: 396.48
Alignments per period: 230
Topology: aaBAbaBAbaBAbabABabAAbaBAbaBAbaBABabABabABaaBAbaBAbaBAbabABabABabAAbaBAbaBAbabABabABabABaaBAbaBABabABabABabAAbaBAbaBAbabABabABabAAbaBAbaBAbaBABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 1.923)
Loop closure: 1.5×10⁻²⁴

Neighbours on the map

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