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II.C.39

m₃ = 0.5

From Li & Liao (2017)

II.C.39 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 65.167 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 6886), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00406 of each other at a top speed of 18.2, line up 54 times a period, and the computed loop closes to 1.5×10⁻²⁵.

Measured over one period

Period: 65.16708519
Masses: 1 : 1 : 0.5
Energy: -0.824576
Angular momentum: 0
Closest approach: 0.004062
Top speed: 18.16
Path length: 149.37
Alignments per period: 54
Stability: unstable (|λ|max 6886)
Loop closure: 1.5×10⁻²⁵

Neighbours on the map

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