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II.C.3

m₃ = 4

From Li & Liao (2017)

II.C.3 m₃ = 4 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 4 that return to their starting positions and velocities every 64.175 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 16.84), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000185 of each other at a top speed of 186, line up 180 times a period, and the computed loop closes to 6.4×10⁻²⁵.

Measured over one period

Period: 64.17466631
Masses: 1 : 1 : 4
Energy: -6.58349
Angular momentum: 0
Closest approach: 1.9×10⁻⁴
Top speed: 186.1
Path length: 260.39
Alignments per period: 180
Stability: unstable (|λ|max 16.84)
Loop closure: 6.4×10⁻²⁵

Neighbours on the map

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