Atlas2,064 of 3,942

II.C.245

m₃ = 0.5

From Li & Liao (2017)

II.C.245 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 184.15 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 0.00000907 of each other at a top speed of 383, line up 310 times a period, and the computed loop closes to 4.1×10⁻²¹.

Measured over one period

Period: 184.1495051
Masses: 1 : 1 : 0.5
Energy: -1.15814
Angular momentum: 0
Closest approach: 9.1×10⁻⁶
Top speed: 383.3
Path length: 435.99
Alignments per period: 310
Topology: ababAbaBABaBABabABabaBabaBAbABAbaBAbabAbabABabABabABAbaBAbaBAbaBABaBABabABabABabaBAbaBAbaBAbaBAbabABabABabABabaBAbaBAbaBAbaBAbabABabABabABAbABAbaBAbaBAbaBABabABabABabaBabaBAbaBABaBAbabAbabABabABAbABAbaB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 4.1×10⁻²¹

Neighbours on the map

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