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II.C.3

m₃ = 2

From Li & Liao (2017)

II.C.3 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 8.4364 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 4271), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0042 of each other at a top speed of 24.8, line up 22 times a period, and the computed loop closes to 6.4×10⁻²⁶.

Measured over one period

Period: 8.436435880
Masses: 1 : 1 : 2
Energy: -3.81002
Angular momentum: 0
Closest approach: 0.004201
Top speed: 24.82
Path length: 27.425
Alignments per period: 22
Stability: unstable (|λ|max 4271)
Loop closure: 6.4×10⁻²⁶

Neighbours on the map

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