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II.B.3

m₃ = 4

From Li, Jing & Liao (2018)

II.B.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 159.16 time units, published by Li, Jing & Liao (2018). Class II.B orbits, mostly long-period. It is weakly unstable (largest Floquet multiplier 1.047), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000994 of each other at a top speed of 802, line up 512 times a period, and the computed loop closes to 3.7×10⁻²¹.

Measured over one period

Period: 159.1584664
Masses: 1 : 1 : 4
Energy: -7.19268
Angular momentum: 0
Closest approach: 9.9×10⁻⁶
Top speed: 802.4
Path length: 614.36
Alignments per period: 512
Topology: abababababababABABABABABABAbababababababABABABABABABAbababababababaBABABABABABABababababababaBABABABABABABAbababababababABABABABABABAbababababababaBABABABABABABababababababaBABABABABABABabababababababABABABABABABAbababababababABABABABABABABababababababaBABABABABABAB (free-group class)
Stability: weakly unstable (|λ|max 1.047)
Loop closure: 3.7×10⁻²¹

Neighbours on the map

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