  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 and
provides details and explanations for these Resolutions. It is explained why
they present significant progress over the corresponding IAU 1991 Resolutions
and why they are necessary in the light of present accuracies in astrometry,
celestial mechanics and metrology. In fact most of these Resolutions are
consistent with astronomical models and software already in use.
  The metric tensors and gravitational potentials of both the Barycentric
Celestial Reference System and Geocentric Celestial Reference System are
defined and discussed. The necessity and relevance of the two celestial
reference systems are explained. The transformations of coordinates and
gravitational potentials are discussed. Potential coefficients parameterizing
the post-Newtonian gravitational potentials are expounded. Simplified versions
of the time transformations suitable for modern clock accuracies are
elucidated. Various approximations used in the Resolutions are explicated and
justified. Some models (e.g. for higher spin moments) that serve the purpose
for estimating orders of magnitude have actually never been published before.
