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II.C.7

m₃ = 4

From Li & Liao (2017)

II.C.7 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 113.59 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.000196 of each other at a top speed of 181, line up 306 times a period, and the computed loop closes to 1.0×10⁻²⁴.

Measured over one period

Period: 113.5938429
Masses: 1 : 1 : 4
Energy: -6.41242
Angular momentum: 0
Closest approach: 2.0×10⁻⁴
Top speed: 180.8
Path length: 460.30
Alignments per period: 306
Topology: ababababababABABABABABAbabababababaBABABABABABababababababABABABABABAbabababababaBABABABABABababababababABABABABABAbabababababABABABABABABabababababaBABABABABAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 1.0×10⁻²⁴

Neighbours on the map

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