Atlas2,179 of 3,942

II.C.112

m₃ = 0.5

From Li & Liao (2017)

II.C.112 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 98.207 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 34.99), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000393 of each other at a top speed of 58.2, line up 152 times a period, and the computed loop closes to 9.8×10⁻²⁵.

Measured over one period

Period: 98.20722374
Masses: 1 : 1 : 0.5
Energy: -1.11519
Angular momentum: 0
Closest approach: 3.9×10⁻⁴
Top speed: 58.21
Path length: 240.73
Alignments per period: 152
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabAbabABabABabABabABabABabABabABabABabABabABabAAbbAB (free-group class)
Stability: unstable (|λ|max 34.99)
Loop closure: 9.8×10⁻²⁵

Neighbours on the map

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