Atlas2,207 of 3,942

II.C.157

m₃ = 0.5

From Li & Liao (2017)

II.C.157 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 142.53 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 4.791), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000186 of each other at a top speed of 84.6, line up 200 times a period, and the computed loop closes to 5.1×10⁻²⁴.

Measured over one period

Period: 142.5318373
Masses: 1 : 1 : 0.5
Energy: -1.03409
Angular momentum: 0
Closest approach: 1.9×10⁻⁴
Top speed: 84.61
Path length: 326.45
Alignments per period: 200
Topology: ababAbaBABaBAbabAbabABaBABabABabABabABabABabABabABAbABAbaBAbaBAbaBAbaBAbaBAbaBAbaBABaBABabABabABabABabABabABabABAbABabaBabaBAbABAbaB (free-group class)
Stability: weakly unstable (|λ|max 4.791)
Loop closure: 5.1×10⁻²⁴

Neighbours on the map

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