Atlas375 of 3,942

I.A.87

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.87 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 123.64 time units, published by Li, Jing & Liao (2018). Class I.A orbits found with Liao’s clean numerical simulation method, for a third body of varying mass. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.00000994 of each other at a top speed of 339, line up 286 times a period, and the computed loop closes to 3.0×10⁻¹⁶.

Measured over one period

Period: 123.6422147
Masses: 1 : 1 : 0.75
Energy: -1.84232
Angular momentum: 0
Closest approach: 9.9×10⁻⁶
Top speed: 339.0
Path length: 320.27
Alignments per period: 286
Topology: ababAbabaBABabABABabaBAbabaBABabABABabaBAbabaBAbabABABabABAbabaBAbabABABabABAbabaBababABABaBABAbabABababABAbaBABAbabABababABAbaBABAbaBABababABabaBABAbaBABababABabaBABAbABAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 3.0×10⁻¹⁶

Neighbours on the map

All I.A orbits, the families of periodic three-body orbits, or the atlas map.