Atlas1,373 of 3,942

II.B.6

m₃ = 0.75

From Li, Jing & Liao (2018)

II.B.6 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 181.8 time units, published by Li, Jing & Liao (2018). Class II.B orbits, mostly long-period. It is unstable (largest Floquet multiplier 1016), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000789 of each other at a top speed of 38.1, line up 144 times a period, and the computed loop closes to 8.0×10⁻²⁵.

Measured over one period

Period: 181.8029931
Masses: 1 : 1 : 0.75
Energy: -0.939603
Angular momentum: 0
Closest approach: 7.9×10⁻⁴
Top speed: 38.11
Path length: 393.68
Alignments per period: 144
Topology: abaBabaBAbaBAbaBAbabAbabABabABabABabaBAbaBAbaBAbabAbabABabABabABabaBabaBAbaBAbaBAbabABabABabAB (free-group class)
Stability: unstable (|λ|max 1016)
Loop closure: 8.0×10⁻²⁵

Neighbours on the map

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