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II.C.6

m₃ = 0.5

From Li & Liao (2017)

II.C.6 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 10.676 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 5.294), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000843 of each other at a top speed of 39.7, line up 24 times a period, and the computed loop closes to 7.8×10⁻²⁶.

Measured over one period

Period: 10.67649562
Masses: 1 : 1 : 0.5
Energy: -1.42647
Angular momentum: 0
Closest approach: 8.4×10⁻⁴
Top speed: 39.74
Path length: 27.720
Alignments per period: 24
Stability: weakly unstable (|λ|max 5.294)
Loop closure: 7.8×10⁻²⁶

Neighbours on the map

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