Atlas2,033 of 3,942

II.C.224

m₃ = 0.5

From Li & Liao (2017)

II.C.224 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 180.35 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 1.000), so a small nudge only makes it wobble. The bodies pass within 0.00000698 of each other at a top speed of 437, line up 252 times a period, and the computed loop closes to 5.9×10⁻²¹.

Measured over one period

Period: 180.3452657
Masses: 1 : 1 : 0.5
Energy: -1.05227
Angular momentum: 0
Closest approach: 7.0×10⁻⁶
Top speed: 437.2
Path length: 436.56
Alignments per period: 252
Topology: aaBAbaBAbaBAbabABabABabABabAAbaBAbaBAbaBAbabABabABabABaaBAbaBAbaBAbaBAbabABabABabAAbaBAbaBAbaBAbaBABabABabABabAAbaBAbaBAbaBAbabABabABabABabAAbaBAbaBAbaBABabABabABabAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 5.9×10⁻²¹

Neighbours on the map

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