Atlas593 of 3,942

I.A.116

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.116 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 124.26 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 1.596), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000601 of each other at a top speed of 47, line up 242 times a period, and the computed loop closes to 8.1×10⁻²⁵.

Measured over one period

Period: 124.2585707
Masses: 1 : 1 : 0.5
Energy: -1.30778
Angular momentum: 0
Closest approach: 6.0×10⁻⁴
Top speed: 47.05
Path length: 323.53
Alignments per period: 242
Topology: aabAbaBABabAbabABaBAAbbABaaBAbbAAbaBBaabAbaBABaBAbabABaBAAbbABaaBBabAAbaBBaabAbbAABaBAbabABaBABabAbaaBBabAAbaBBaaBAbbAABaBAbabAbaBABabAbaaBBabAAbbABaaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 1.596)
Loop closure: 8.1×10⁻²⁵

Neighbours on the map

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