Atlas2,209 of 3,942

II.C.33

m₃ = 0.5

From Li & Liao (2017)

II.C.33 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 48.808 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 1.528), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000132 of each other at a top speed of 1, line up 58 times a period, and the computed loop closes to 2.2×10⁻²⁴.

Measured over one period

Period: 48.80841958
Masses: 1 : 1 : 0.5
Energy: -0.921672
Angular momentum: 0
Closest approach: 1.3×10⁻⁴
Top speed: 100.3
Path length: 101.36
Alignments per period: 58
Topology: ababAbabABaBABabABAbABabaBababAbABABaB (free-group class)
Stability: weakly unstable (|λ|max 1.528)
Loop closure: 2.2×10⁻²⁴

Neighbours on the map

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