Atlas1,558 of 3,942

II.C.41

m₃ = 0.75

From Li & Liao (2017)

II.C.41 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 81.781 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 59.62), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0202 of each other at a top speed of 7.45, line up 74 times a period, and the computed loop closes to 1.1×10⁻²⁶.

Measured over one period

Period: 81.78053559
Masses: 1 : 1 : 0.75
Energy: -1.02408
Angular momentum: 0
Closest approach: 0.02018
Top speed: 7.453
Path length: 184.28
Alignments per period: 74
Topology: abaBabaBAbaBAbabAbabABabABabaBAbaBAbaBAbabABabAB (free-group class)
Stability: unstable (|λ|max 59.62)
Loop closure: 1.1×10⁻²⁶

Neighbours on the map

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