The definition of the Galactic coordinate system was announced by the IAU Sub-Commission 33b on behalf of the IAU in 1958. For more than 50 years the definition of the Galactic coordinate system has remained unchanged from this IAU1958 version. On the basis of deep and all-sky catalogs, the position of the Galactic plane can be revised and updated definitions of the Galactic coordinate systems can be proposed. We re-determine the position of the Galactic plane based on modern large catalogs, such as the Two Micron All-Sky Survey (2MASS) and the SPECFIND v2.0. This paper also aims to propose a possible definition of the optimal Galactic coordinate system by adopting the ICRS position of the Sgr A* at the Galactic center. The near-infrared 2MASS point source catalog and the SPECFIND v2.0 catalog of radio continuum spectra are used to determine the mean position of the Galactic plane on the celestial sphere. By fitting the data to an ideal Galactic equator, the parameters defining the Galactic coordinate system are obtained. We find that the obliquity of the Galactic equator on the ICRS principal plane is about $0.4^circ$ (2MASS) and $0.6^circ$ (SPECFIND v2.0) larger than the J2000.0 value, which is widely used in coordinate transformations between the equatorial $(alpha, delta)$ and the Galactic $(ell, b)$. Depending on the adopted parameters, data, and methods, the largest difference between the resulting Galactic coordinate systems is several arcminutes. We derive revised transformation matrices and parameters describing the orientation of the Galactic coordinate systems in the ICRS at the 1 milli-arcsecond level to match the precision of modern observations. For practical applications, we propose that a revised definition of the Galactic coordinate system should be required in the near future.
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