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II.C.6

m₃ = 5

From Li & Liao (2017)

II.C.6 m₃ = 5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 5 that return to their starting positions and velocities every 105.65 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 0.00000579 of each other at a top speed of 12, line up 380 times a period, and the computed loop closes to 6.5×10⁻¹⁸.

Measured over one period

Period: 105.6505055
Masses: 1 : 1 : 5
Energy: -9.03648
Angular momentum: 0
Closest approach: 5.8×10⁻⁶
Top speed: 1200
Path length: 450.40
Alignments per period: 380
Stability: stable (|λ|max 1.000)
Loop closure: 6.5×10⁻¹⁸

Neighbours on the map

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