Atlas1,359 of 3,942

II.B.7

m₃ = 0.75

From Li, Jing & Liao (2018)

II.B.7 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 119.05 time units, published by Li, Jing & Liao (2018). Class II.B orbits, mostly long-period. It is unstable (largest Floquet multiplier 15.71), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000946 of each other at a top speed of 34.8, line up 164 times a period, and the computed loop closes to 8.3×10⁻²⁵.

Measured over one period

Period: 119.0524139
Masses: 1 : 1 : 0.75
Energy: -1.35315
Angular momentum: 0
Closest approach: 9.5×10⁻⁴
Top speed: 34.82
Path length: 307.78
Alignments per period: 164
Topology: abaBabaBAbaBAbabABabABabaBabaBAbaBAbabABabABabaBAbaBAbabAbabABabABabaBAbaBAbabAbabABabABabaBAbaBAbabABabAB (free-group class)
Stability: unstable (|λ|max 15.71)
Loop closure: 8.3×10⁻²⁵

Neighbours on the map

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