Atlas2,162 of 3,942

II.C.247

m₃ = 0.5

From Li & Liao (2017)

II.C.247 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 198.08 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 183.1), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00022 of each other at a top speed of 77.8, line up 326 times a period, and the computed loop closes to 2.2×10⁻²³.

Measured over one period

Period: 198.0785646
Masses: 1 : 1 : 0.5
Energy: -1.15289
Angular momentum: 0
Closest approach: 2.2×10⁻⁴
Top speed: 77.80
Path length: 481.02
Alignments per period: 326
Topology: abaBabaBAbaBAbaBAbaBAbaBAbaBAbabAbaBABaBAbabAbaBABaBAbabAbabABaBABabAbabABabABabABabABabABabABabABabABabABabaBabABAbABabaBabaBAbABAbaBabaBAbABAbaBabaBAbaBAbaBAbaBAbaBAbaBAbabAbabABabABabABabABabABabABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 183.1)
Loop closure: 2.2×10⁻²³

Neighbours on the map

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