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II.C.13

m₃ = 4

From Li & Liao (2017)

II.C.13 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 129.36 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 1.004), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000003 of each other at a top speed of 1462, line up 412 times a period, and the computed loop closes to 4.7×10⁻²¹.

Measured over one period

Period: 129.3612607
Masses: 1 : 1 : 4
Energy: -7.14393
Angular momentum: 0
Closest approach: 3.0×10⁻⁶
Top speed: 1462
Path length: 492.75
Alignments per period: 412
Topology: 0 (free-group class)
Stability: weakly unstable (|λ|max 1.004)
Loop closure: 4.7×10⁻²¹

Neighbours on the map

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