Atlas1,808 of 3,942

II.C.131

m₃ = 0.75

From Li & Liao (2017)

II.C.131 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 129.05 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 19.16), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00015 of each other at a top speed of 87.1, line up 196 times a period, and the computed loop closes to 2.9×10⁻²⁴.

Measured over one period

Period: 129.0520294
Masses: 1 : 1 : 0.75
Energy: -1.44057
Angular momentum: 0
Closest approach: 1.5×10⁻⁴
Top speed: 87.13
Path length: 343.62
Alignments per period: 196
Topology: abaBabaBAbabAbabABabaBAbaBAbabABabaBabaBAbabAbabABabABabaBabaBAbabAbabABabaBAbaBAbabABabaBabaBAbabAbabABabABabaBAbaBAbabABabAB (free-group class)
Stability: unstable (|λ|max 19.16)
Loop closure: 2.9×10⁻²⁴

Neighbours on the map

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