Atlas612 of 3,942

I.A.56

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.56 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 70.752 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 3.777), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000287 of each other at a top speed of 68.1, line up 134 times a period, and the computed loop closes to 1.7×10⁻²⁴.

Measured over one period

Period: 70.75221974
Masses: 1 : 1 : 0.5
Energy: -1.29373
Angular momentum: 0
Closest approach: 2.9×10⁻⁴
Top speed: 68.09
Path length: 184.51
Alignments per period: 134
Topology: aabAbaBAAbbAbaaBAbbAABaBAbabABaBAAbbABaaBAbbAABaBAbaaBBaBAAbaBBaabAbaBABabAbaaBBabAAbaBB (free-group class)
Stability: weakly unstable (|λ|max 3.777)
Loop closure: 1.7×10⁻²⁴

Neighbours on the map

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