Atlas613 of 3,942

I.A.98

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.98 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 110.51 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 5.155), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000333 of each other at a top speed of 63.2, line up 210 times a period, and the computed loop closes to 3.4×10⁻²⁴.

Measured over one period

Period: 110.5070751
Masses: 1 : 1 : 0.5
Energy: -1.29568
Angular momentum: 0
Closest approach: 3.3×10⁻⁴
Top speed: 63.19
Path length: 288.21
Alignments per period: 210
Topology: aabAbaBAAbbAbaaBAbbAABaBAbabABaBAAbbABaaBAbbAABaBAbabABaBAAbbABaaBAbbAABaBAbaaBBaBAAbaBBaabAbaBABabAbaaBBabAAbaBBaabAbaBABabAbaaBBabAAbaBB (free-group class)
Stability: weakly unstable (|λ|max 5.155)
Loop closure: 3.4×10⁻²⁴

Neighbours on the map

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