Atlas283 of 3,942

I.A.78

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.78 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 105.27 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 0.00000881 of each other at a top speed of 389, line up 174 times a period, and the computed loop closes to 5.7×10⁻²¹.

Measured over one period

Period: 105.2715050
Masses: 1 : 1 : 0.5
Energy: -1.13496
Angular momentum: 0
Closest approach: 8.8×10⁻⁶
Top speed: 389.0
Path length: 242.77
Alignments per period: 174
Topology: abaBAbaBAbabABabABabaBAbaBAbabABabABabaBAbaBAbabABabABabABAbaBAbaBABabABabABAbaBAbaBABabABabABAbaBAbaBABabABabAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 5.7×10⁻²¹

Neighbours on the map

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