Atlas373 of 3,942

I.A.30

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.30 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 81.343 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 7.428), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000675 of each other at a top speed of 41.1, line up 106 times a period, and the computed loop closes to 6.3×10⁻¹⁸.

Measured over one period

Period: 81.34330057
Masses: 1 : 1 : 0.75
Energy: -1.25926
Angular momentum: 0
Closest approach: 6.8×10⁻⁴
Top speed: 41.08
Path length: 182.90
Alignments per period: 106
Topology: ababABabaBABabaBABabABABabaBAbabABABabABAbabABAbabABababABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 7.428)
Loop closure: 6.3×10⁻¹⁸

Neighbours on the map

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