Atlas1,886 of 3,942

II.C.31

m₃ = 0.75

From Li & Liao (2017)

II.C.31 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 44.797 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 21.63), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00833 of each other at a top speed of 11.8, line up 62 times a period, and the computed loop closes to 4.1×10⁻²⁷.

Measured over one period

Period: 44.79716484
Masses: 1 : 1 : 0.75
Energy: -1.35630
Angular momentum: 0
Closest approach: 0.008329
Top speed: 11.76
Path length: 115.85
Alignments per period: 62
Topology: abaBabaBAbabAbabABabABabaBAbaBAbabABabAB (free-group class)
Stability: unstable (|λ|max 21.63)
Loop closure: 4.1×10⁻²⁷

Neighbours on the map

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