Atlas388 of 3,942

I.A.87

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.87 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 100.1 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 0.0000837 of each other at a top speed of 126, line up 190 times a period, and the computed loop closes to 6.3×10⁻²⁴.

Measured over one period

Period: 100.0973396
Masses: 1 : 1 : 0.5
Energy: -1.25592
Angular momentum: 0
Closest approach: 8.4×10⁻⁵
Top speed: 126.2
Path length: 245.21
Alignments per period: 190
Topology: abaBabaBAbaBAbaBAbabAbabABabABAbABabaBabaBAbaBABaBABabAbabABabABAbABAbaBAbaBAbaBABaBABabABabaBabABAbABAbaBAbabAbabABaBABabAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 6.3×10⁻²⁴

Neighbours on the map

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