Atlas637 of 3,942

I.A.6

m₃ = 0.75

From Li, Jing & Liao (2018)

I.A.6 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 10.532 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 1572), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00243 of each other at a top speed of 21.5, line up 26 times a period, and the computed loop closes to 2.4×10⁻²⁵.

Measured over one period

Period: 10.53232071
Masses: 1 : 1 : 0.75
Energy: -1.95897
Angular momentum: 0
Closest approach: 0.002431
Top speed: 21.50
Path length: 27.394
Alignments per period: 26
Topology: aaabAbbAAABaBB (free-group class)
Stability: unstable (|λ|max 1572)
Loop closure: 2.4×10⁻²⁵

Neighbours on the map

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