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II.C.40

m₃ = 0.5

From Li & Liao (2017)

II.C.40 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 30.612 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 62.06), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000192 of each other at a top speed of 83.3, line up 64 times a period, and the computed loop closes to 9.9×10⁻²⁵.

Measured over one period

Period: 30.61215454
Masses: 1 : 1 : 0.5
Energy: -1.38270
Angular momentum: 0
Closest approach: 1.9×10⁻⁴
Top speed: 83.26
Path length: 84.339
Alignments per period: 64
Topology: aabAbbAABabABabABabAAbaBAbaBAbabABabABabAB (free-group class)
Stability: unstable (|λ|max 62.06)
Loop closure: 9.9×10⁻²⁵

Neighbours on the map

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