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II.C.1

m₃ = 0.5

From Li & Liao (2017)

II.C.1 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 16.448 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 12.3), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0204 of each other at a top speed of 7.03, line up 14 times a period, and the computed loop closes to 5.8×10⁻²⁸.

Measured over one period

Period: 16.44824527
Masses: 1 : 1 : 0.5
Energy: -0.864684
Angular momentum: 0
Closest approach: 0.02038
Top speed: 7.033
Path length: 35.044
Alignments per period: 14
Topology: aaBAbaBAB (free-group class)
Stability: unstable (|λ|max 12.30)
Loop closure: 5.8×10⁻²⁸

Neighbours on the map

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