Atlas2,199 of 3,942

II.C.196

m₃ = 0.5

From Li & Liao (2017)

II.C.196 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 154.28 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is linearly stable (largest Floquet multiplier 1.024), so a small nudge only makes it wobble. The bodies pass within 0.0000401 of each other at a top speed of 182, line up 236 times a period, and the computed loop closes to 1.0×10⁻¹⁶.

Measured over one period

Period: 154.2765378
Masses: 1 : 1 : 0.5
Energy: -1.09636
Angular momentum: 0
Closest approach: 4.0×10⁻⁵
Top speed: 182.4
Path length: 368.23
Alignments per period: 236
Topology: abaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABabABabABabABabABabABAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabABabABabAB (free-group class)
Stability: stable (|λ|max 1.024)
Loop closure: 1.0×10⁻¹⁶

Neighbours on the map

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