We discuss the IAU resolutions B1.3, B1.4, B1.5, and B1.9 that were adopted during the 24th General Assembly in Manchester, 2000, and provides details on 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 the 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 of estimating orders of magnitude have actually never been published before.

Primary cesium frequency standards provide physical realizations of the second of the International System of Units, and these are compared with the scale unit of time scales. A method of combining the data from several standards is presented. As an example, this method is applied to the International Atomic Time scale using all the available data from primary standards.

This paper reviews the theoretical motivation for the leap second in the context of the historical evolution of time measurement. The periodic insertion of a leap second step into the scale of Coordinated Universal Time (UTC) necessitates frequent changes in complex timekeeping systems and is currently the subject of discussion in working groups of various international scienti c organizations. UTC is an atomic time scale that agrees in rate with International Atomic Time (TAI), but differs by an integral number of seconds, and is the basis of civil time. In contrast, Universal Time (UT1) is an astronomical time scale de ned by the Earth's rotation and is used in celestial navigation. UTC is presently maintained to within 0.9 s of UT1. As the needs of celestial navigation that depend on UT1 can now be met by satellite systems, such as the Global Positioning System (GPS), options for revising the de nition of UTC and the possible role of leap seconds in the future are considered.

This paper summarizes the creation and technical evolution of atomic time scales, recalling the parallel development of their acceptance and the remaining problems. We consider a consequence of the accuracy of time measurement, i.e. the entry of Einstein's general relativity into metrology and its applications. We give some details about the method of calculation and the characteristics of International Atomic Time, and we show how it is disseminated at the ultimate level of precision.

Abstract-Frequency differences between major national timing centers are being resolved with uncertainty of less than 1 part in 1014',using satellites of the Global Positioning System (GPS) in common-view. Portable clock and GPS time differences are in excellent agreement. Around the world GPS measurement between three laboratories had a time residual of 5.1 ns.