Atlas2,148 of 3,942

II.C.204

m₃ = 0.5

From Li & Liao (2017)

II.C.204 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 158.57 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 1.597), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000534 of each other at a top speed of 158, line up 238 times a period, and the computed loop closes to 1.7×10⁻²³.

Measured over one period

Period: 158.5702051
Masses: 1 : 1 : 0.5
Energy: -1.09378
Angular momentum: 0
Closest approach: 5.3×10⁻⁵
Top speed: 158.1
Path length: 385.78
Alignments per period: 238
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabABabABaaBBabAAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbabABaBABabABabABabABabABabABabABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 1.597)
Loop closure: 1.7×10⁻²³

Neighbours on the map

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