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II.C.45

m₃ = 2

From Li & Liao (2017)

II.C.45 m₃ = 2 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 2 that return to their starting positions and velocities every 138.35 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 1.333), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000164 of each other at a top speed of 404, line up 258 times a period, and the computed loop closes to 6.5×10⁻²².

Measured over one period

Period: 138.3471807
Masses: 1 : 1 : 2
Energy: -3.10915
Angular momentum: 0
Closest approach: 1.6×10⁻⁵
Top speed: 403.6
Path length: 410.20
Alignments per period: 258
Stability: weakly unstable (|λ|max 1.333)
Loop closure: 6.5×10⁻²²

Neighbours on the map

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