Atlas497 of 3,942

I.A.57

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.57 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 113.68 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 weakly unstable (largest Floquet multiplier 4.097), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000212 of each other at a top speed of 73.4, line up 174 times a period, and the computed loop closes to 9.2×10⁻¹⁸.

Measured over one period

Period: 113.6756253
Masses: 1 : 1 : 0.75
Energy: -1.42376
Angular momentum: 0
Closest approach: 2.1×10⁻⁴
Top speed: 73.37
Path length: 287.18
Alignments per period: 174
Topology: abaBAbabABabaBAbabABabaBABabABAbabABabaBAbabABabaBAbabABAbaBABabABAbaBABabABAbabABabaBABabABAbaBABabABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 4.097)
Loop closure: 9.2×10⁻¹⁸

Neighbours on the map

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