Atlas495 of 3,942

I.A.78

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.78 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 153.79 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 0.0000677 of each other at a top speed of 13, line up 226 times a period, and the computed loop closes to 1.6×10⁻¹⁶.

Measured over one period

Period: 153.7854226
Masses: 1 : 1 : 0.75
Energy: -1.38419
Angular momentum: 0
Closest approach: 6.8×10⁻⁵
Top speed: 129.9
Path length: 382.15
Alignments per period: 226
Topology: abaBAbabABabaBAbabABAbaBABabABAbabABabaBAbabABAbaBABabABAbabABabaBAbabABAbaBABabABAbaBABabaBAbabABabaBABabABAbaBABabaBAbabABabaBABabABAbaBAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 1.6×10⁻¹⁶

Neighbours on the map

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