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This paper discusses the IAU Resolutions B1.3, B1.4, B1.5 and B1.9 (2000)that were adopted during the 24th General Assembly in Manchester, 2000 andprovides details and explanations for these Resolutions. It is explained whythey present significant progress over the corresponding IAU 1991 Resolutionsand why they are necessary in the light of present accuracies in astrometry,celestial mechanics and metrology. In fact most of these Resolutions areconsistent with astronomical models and software already in use.  The metric tensors and gravitational potentials of both the BarycentricCelestial Reference System and Geocentric Celestial Reference System aredefined and discussed. The necessity and relevance of the two celestialreference systems are explained. The transformations of coordinates andgravitational potentials are discussed. Potential coefficients parameterizingthe post-Newtonian gravitational potentials are expounded. Simplified versionsof the time transformations suitable for modern clock accuracies areelucidated. Various approximations used in the Resolutions are explicated andjustified. Some models (e.g. for higher spin moments) that serve the purposefor estimating orders of magnitude have actually never been published before.Comment: 45 pages, 1 figure, submitted to Astronomical Journa

The IAU 2000 Resolutions for Astrometry, Celestial Mechanics, and Metrology in the Relativistic Framework: Explanatory Supplement