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II.B.5

m₃ = 0.75

From Li, Jing & Liao (2018)

II.B.5 m₃ = 0.75 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.75 that return to their starting positions and velocities every 84.177 time units, published by Li, Jing & Liao (2018). Class II.B orbits, mostly long-period. It is unstable (largest Floquet multiplier 76.88), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00212 of each other at a top speed of 23.1, line up 140 times a period, and the computed loop closes to 1.3×10⁻²⁶.

Measured over one period

Period: 84.17730670
Masses: 1 : 1 : 0.75
Energy: -1.53049
Angular momentum: 0
Closest approach: 0.002118
Top speed: 23.15
Path length: 230.70
Alignments per period: 140
Topology: abaBabaBAbabABabABabaBAbaBAbabABabaBabaBAbaBAbabAbabABabaBAbaBAbabABabABabaBAbabAbabABabAB (free-group class)
Stability: unstable (|λ|max 76.88)
Loop closure: 1.3×10⁻²⁶

Neighbours on the map

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