Atlas490 of 3,942

I.A.35

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.35 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 87.682 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 unstable (largest Floquet multiplier 282), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00163 of each other at a top speed of 28.6, line up 106 times a period, and the computed loop closes to 5.4×10⁻²⁵.

Measured over one period

Period: 87.68218193
Masses: 1 : 1 : 0.5
Energy: -0.953001
Angular momentum: 0
Closest approach: 0.001635
Top speed: 28.57
Path length: 197.61
Alignments per period: 106
Topology: aabAbaBABabABabABabABabABabABaaBAbbAABaBAbabABabABabABabABabABabAAbaBB (free-group class)
Stability: unstable (|λ|max 282.0)
Loop closure: 5.4×10⁻²⁵

Neighbours on the map

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