Atlas625 of 3,942

I.A.53

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.53 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 98.773 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 5.905), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000161 of each other at a top speed of 91, line up 126 times a period, and the computed loop closes to 2.5×10⁻²⁴.

Measured over one period

Period: 98.77256712
Masses: 1 : 1 : 0.5
Energy: -1.00338
Angular momentum: 0
Closest approach: 1.6×10⁻⁴
Top speed: 91.05
Path length: 237.59
Alignments per period: 126
Topology: aaBAbabABabABaaBAbaBABabABaaBAbaBABabABabAAbaBABabABabAAbaBAbabABabAAbaBAbabABabAB (free-group class)
Stability: weakly unstable (|λ|max 5.905)
Loop closure: 2.5×10⁻²⁴

Neighbours on the map

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