Atlas1,555 of 3,942

II.C.119

m₃ = 0.75

From Li & Liao (2017)

II.C.119 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 186.13 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 9268), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00394 of each other at a top speed of 17, line up 176 times a period, and the computed loop closes to 2.7×10⁻²⁵.

Measured over one period

Period: 186.1251012
Masses: 1 : 1 : 0.75
Energy: -1.05395
Angular momentum: 0
Closest approach: 0.003936
Top speed: 16.97
Path length: 424.91
Alignments per period: 176
Topology: abaBabaBAbabAbabABabABabaBabaBAbaBAbabABabABabABabaBAbaBAbabAbabABabABabaBabaBAbabAbabABabABabaBAbaBAbaBAbabABabAB (free-group class)
Stability: unstable (|λ|max 9268)
Loop closure: 2.7×10⁻²⁵

Neighbours on the map

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