Atlas1,756 of 3,942

II.C.109

m₃ = 0.75

From Li & Liao (2017)

II.C.109 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 109.89 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 944.5), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000303 of each other at a top speed of 61.3, line up 154 times a period, and the computed loop closes to 2.2×10⁻²⁴.

Measured over one period

Period: 109.8857438
Masses: 1 : 1 : 0.75
Energy: -1.37152
Angular momentum: 0
Closest approach: 3.0×10⁻⁴
Top speed: 61.33
Path length: 286.72
Alignments per period: 154
Topology: abaBabaBAbabAbabABabABabaBabaBAbaBAbabAbabABabABabaBabaBAbaBAbabAbabABabABabaBabaBAbaBAbabAbabABabAB (free-group class)
Stability: unstable (|λ|max 944.5)
Loop closure: 2.2×10⁻²⁴

Neighbours on the map

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