Atlas361 of 3,942

I.A.72

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.72 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 100.37 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 0.000141 of each other at a top speed of 90.2, line up 214 times a period, and the computed loop closes to 8.1×10⁻²⁴.

Measured over one period

Period: 100.3713840
Masses: 1 : 1 : 0.75
Energy: -1.73840
Angular momentum: 0
Closest approach: 1.4×10⁻⁴
Top speed: 90.15
Path length: 255.76
Alignments per period: 214
Topology: ababABababABAbabABAbabABABabABABabaBAbabaBABabABABabABAbabaBAbabABABabABABabaBABabaBABababABababABAbaBABAbabABababABabaBABAbaBAB (free-group class)
Stability: stable (|λ|max 1.011)
Loop closure: 8.1×10⁻²⁴

Neighbours on the map

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