Atlas1,337 of 3,942

II.A.1

m₃ = 4

From Li, Jing & Liao (2018)

II.A.1 m₃ = 4 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 4 that return to their starting positions and velocities every 80.565 time units, published by Li, Jing & Liao (2018). Class II.A orbits with an unequal third mass. It is weakly unstable (largest Floquet multiplier 1.347), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000939 of each other at a top speed of 261, line up 206 times a period, and the computed loop closes to 5.8×10⁻²⁴.

Measured over one period

Period: 80.56468202
Masses: 1 : 1 : 4
Energy: -6.20027
Angular momentum: 0
Closest approach: 9.4×10⁻⁵
Top speed: 261.1
Path length: 327.83
Alignments per period: 206
Topology: abababababaBABABABABAbabababababABABABABABAbabababababABABABABABAbababababaBABABABABABabababababaBABABABABAB (free-group class)
Stability: weakly unstable (|λ|max 1.347)
Loop closure: 5.8×10⁻²⁴

Neighbours on the map

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