Atlas410 of 3,942

I.A.96

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.96 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 180.77 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 1.011), so a small nudge only makes it wobble. The bodies pass within 0.0000665 of each other at a top speed of 131, line up 310 times a period, and the computed loop closes to 3.1×10⁻¹⁶.

Measured over one period

Period: 180.7729773
Masses: 1 : 1 : 0.75
Energy: -1.51608
Angular momentum: 0
Closest approach: 6.7×10⁻⁵
Top speed: 131.1
Path length: 452.61
Alignments per period: 310
Topology: ababABabaBABabaBABabABAbabABAbabABAbabABAbaBABabaBABabaBAbabABAbabABAbabABAbabABabaBABabaBABabABABabABAbabABAbabABabaBABabaBABabaBABabaBAbabABAbabABAbaBABabaBABabaBABabaBABabABAbabABAbabAB (free-group class)
Stability: stable (|λ|max 1.011)
Loop closure: 3.1×10⁻¹⁶

Neighbours on the map

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