Atlas2,102 of 3,942

II.C.41

m₃ = 0.5

From Li & Liao (2017)

II.C.41 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 43.381 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 89.28), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00237 of each other at a top speed of 23.7, line up 64 times a period, and the computed loop closes to 2.4×10⁻²⁵.

Measured over one period

Period: 43.38096544
Masses: 1 : 1 : 0.5
Energy: -1.09562
Angular momentum: 0
Closest approach: 0.002375
Top speed: 23.70
Path length: 107.74
Alignments per period: 64
Topology: aaBAbaBAbaBAbabABabAAbaBAbaBAbaBABabABabAB (free-group class)
Stability: unstable (|λ|max 89.28)
Loop closure: 2.4×10⁻²⁵

Neighbours on the map

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