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II.C.5

m₃ = 4

From Li & Liao (2017)

II.C.5 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 81.064 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 1.002), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000521 of each other at a top speed of 1108, line up 258 times a period, and the computed loop closes to 1.1×10⁻²⁰.

Measured over one period

Period: 81.06407656
Masses: 1 : 1 : 4
Energy: -7.14029
Angular momentum: 0
Closest approach: 5.2×10⁻⁶
Top speed: 1108
Path length: 307.83
Alignments per period: 258
Topology: abababababababABABABABABABAbababababababaBABABABABABABabababababababABABABABABABAbababababababABABABABABABABababababababaBABABABABABAB (free-group class)
Stability: weakly unstable (|λ|max 1.002)
Loop closure: 1.1×10⁻²⁰

Neighbours on the map

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