Atlas1,326 of 3,942

II.A.5

m₃ = 0.5

From Li, Jing & Liao (2018)

II.A.5 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 37.311 time units, published by Li, Jing & Liao (2018). Class II.A orbits with an unequal third mass. It is unstable (largest Floquet multiplier 214.7), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000264 of each other at a top speed of 71.1, line up 82 times a period, and the computed loop closes to 7.5×10⁻²⁵.

Measured over one period

Period: 37.31138903
Masses: 1 : 1 : 0.5
Energy: -1.42566
Angular momentum: 0
Closest approach: 2.6×10⁻⁴
Top speed: 71.11
Path length: 100.57
Alignments per period: 82
Topology: aabAbabABaBAAbbABaaBBaabAbbAABaBABabAbaaBBabAAbbAABaBB (free-group class)
Stability: unstable (|λ|max 214.7)
Loop closure: 7.5×10⁻²⁵

Neighbours on the map

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