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II.C.38

m₃ = 0.5

From Li & Liao (2017)

II.C.38 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 31.08 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 17.75), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00017 of each other at a top speed of 88.5, line up 60 times a period, and the computed loop closes to 7.4×10⁻²⁵.

Measured over one period

Period: 31.07980394
Masses: 1 : 1 : 0.5
Energy: -1.32540
Angular momentum: 0
Closest approach: 1.7×10⁻⁴
Top speed: 88.53
Path length: 82.980
Alignments per period: 60
Stability: unstable (|λ|max 17.75)
Loop closure: 7.4×10⁻²⁵

Neighbours on the map

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