Atlas1,739 of 3,942

II.C.104

m₃ = 0.75

From Li & Liao (2017)

II.C.104 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 108.48 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 224), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000179 of each other at a top speed of 80, line up 144 times a period, and the computed loop closes to 4.8×10⁻²⁵.

Measured over one period

Period: 108.4818234
Masses: 1 : 1 : 0.75
Energy: -1.32569
Angular momentum: 0
Closest approach: 1.8×10⁻⁴
Top speed: 80.05
Path length: 279.01
Alignments per period: 144
Topology: abaBabaBAbaBAbabAbabABabABabABabaBabaBAbaBAbaBAbabABabABabABabABabaBAbaBAbaBAbabAbabABabABabAB (free-group class)
Stability: unstable (|λ|max 224.0)
Loop closure: 4.8×10⁻²⁵

Neighbours on the map

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