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II.C.8

m₃ = 8

From Li & Liao (2017)

II.C.8 m₃ = 8 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 8 that return to their starting positions and velocities every 129.52 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 0.00000975 of each other at a top speed of 1208, line up 604 times a period, and the computed loop closes to 2.4×10⁻²¹.

Measured over one period

Period: 129.5219662
Masses: 1 : 1 : 8
Energy: -14.8205
Angular momentum: 0
Closest approach: 9.8×10⁻⁶
Top speed: 1208
Path length: 708.57
Alignments per period: 604
Topology: abababababababababababababABABABABABABABABABABABABabababababababababababababABABABABABABABABABABABABABabababababababababababababABABABABABABABABABABABABAbababababababababababababaBABABABABABABABABABABABABAbababababababababababababaBABABABABABABABABABABABABabababababababababababababABABABABABABABABABABABABAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 2.4×10⁻²¹

Neighbours on the map

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