Information about positions and velocities of stars that will be gained in the era of GAIA is crucial for determining dynamical structure in our Galaxy. The distribution function of all component objects in our Galaxy is fundamental for describing its dynamics. However, only the distribution function of observable stars is obtained from space astrometry observations, and it is therefore necessary to develop theoretical studies of how to construct the distribution function of all matter including dark matter and unobservable stars using astrometric data of observable stars. This procedure falls into three categories.

We present a new method for constructing equilibrium phase models for stellar systems. Applications of the iterative method include both modelling of observational data and the construction of initial condition for N-body simulations.

Responsibility for the definition of time scales left the astronomical community some 40 years ago when, in 1967, the second became defined by an atomic transition in the International System of units SI and when International Atomic Time (TAI) was defined as the primary international time scale in 1971.

Monitoring the Earth rotation is essential in various domains linked to reference frames firstly with applications in orbit determination, space geodesy or Astronomy. Secondly for geophysical studies where are involved mass motions within the different external fluid layers, atmosphere, hydrosphere, core and mantle of the earth, this on time scales ranging from a few hours to decades. The Earth Orientation Centre of the IERS is continuously monitoring the earth orientation variations from results derived from the various astro-geodetic techniques. It has in particular the task of deriving an optimal combined series of UT1 which is now based mainly on Very Long Baseline Interferometry (VLBI) with some contribution of LOD derived from GPS. We give here a brief summary concerning the contribution of the various techniques to UT1 and in aprticular how the use of LOD derived from GPS can improve the combination. More details are available in Gambis (2004) and Bizouard and Gambis (2009) and the website http://hpiers.obspm.fr/eop-pc/

It was shown that the ICRF radio sources including the defining sources have significant apparent motion that leads to rotation of the ICRF. This rotation is transformed to secular variations of EOP that is decreased or removed if motion of sources is took into account.

The influence of post-Newtonian effects in the rotation of Earth on UT1 are investigated and found to be negligible.

We present a new solution of Earth Orientation Parameters, based on optical astrometry and catalog EOC-4.

We recall the concepts and nomenclature associated with the IAU 2000 definition of UT1 as function of the Earth rotation angle (ERA). We comment on the complications that arise when UT1 is regarded as both an angle and a time scale. We review the IAU 2006 expressions for the position of the celestial intermediate origin (CIO) and the equation of the origins, and the associated CIO and equinox based procedures for the celestial-to-terrestrial transformation.

Geophysical fluids have a major impact on the Earth's rotation. Tidal variations within the oceans are the predominant cause of subdaily length-of-day (lod) variations while those within the solid body of the Earth are a major source of longer period variations; tidal dissipation within the solid Earth and oceans cause a secular change in lod. Fluctuations of the atmospheric winds are the predominant cause of nontidal lod variations on sub-decadal time scales while decadal variations are caused by interactions between the fluid core and mantle.

The Earth rotation rate and consequently universal time (UT1) and length of day (LOD) are periodically affected by solid Earth tides and oceanic tides. Solid Earth tides induce changes with periods from around 5 days to 18.6 years, with the largest amplitudes occurring at fortnightly, monthly, semi-annual and annual periods, and at 18.6 years. The principal variations caused by oceanic tides have diurnal and semi-diurnal periods. For the investigation of the tidal effects with periods of up to 35 days, UT1 series are estimated from VLBI observation data of the time interval 1984–2008. The amplitudes and phases of the terms of interest are calculated and the results for diurnal and sub-diurnal periods are compared and evaluated with tidal variations derived from a GNSS-based LOD time series of 8 months. The observed tidal signals are finally compared to the predicted tidal variations according to recent geophysical models.

Very Long Baseline Interferometry (VLBI) is the only space geodetic technique which is capable of estimating the Earth's phase of rotation, expressed as Universal Time UT1, over time scales of a few days or longer. Satellite-observing techniques like the Global Navigation Satellite Systems (GNSS) are suffering from the fact that Earth rotation is indistinguishable from a rotation of the satellite orbit nodes, which requires the imposition of special procedures to extract UT1 or length of day information. Whereas 24 hour VLBI network sessions are carried out at about three days per week, the hour-long one-baseline intensive sessions (‘Intensives’) are observed from Monday to Friday (INT1) on the baseline Wettzell (Germany) to Kokee Park (Hawaii, U.S.A.), and from Saturday to Sunday on the baseline Tsukuba (Japan) to Wettzell (INT2). Additionally, INT3 sessions are carried out on Mondays between Wettzell, Tsukuba, and Ny-Alesund (Norway), and ultra-rapid e-Intensives between E! urope and Japan also include the baseline Metsähovi (Finland) to Kashima (Japan). The Intensives have been set up to determine daily estimates of UT1 and to be used for UT1 predictions. Because of the short duration and the limited number of stations the observations can nowadays be e-transferred to the correlators, or to a node close to the correlator, and the estimates of UT1 are available shortly after the last observation thus allowing the results to be used for prediction purposes.

The axial component of Earth rotation, which is conventionally expressed by Universal Time (UT1), contains small physical signals with diurnal and subdiurnal periods. This part of the spectrum is dominated by the tidal effects which are regular and predictable. The largest components express the influence of the gravitationally forced ocean tides with diurnal and semidiurnal periods and amplitudes up to 0.02 milliseconds (ms) in UT1 corresponding to an angular displacement of 0.30 milliarcseconds (mas); see Table 8.3 of the IERS Conventions (IERS, 2003). There are also smaller subdiurnal components (amplitudes up to 0.03 mas), designated as “spin libration” by Chao et al. (1991), due to direct influence of the tidal gravitation on those features of the Earth's density distribution which are expressed by the non-zonal terms of the geopotential. These components are not included in the models recommended by the IERS Conventions, in contrast to the corresponding effect in polar motion (ibid., Table 5.1).

Here we consider in detail the subdiurnal libration in UT1. We derive an analytical solution for the structural model of the Earth consisting of an elastic mantle and a liquid core which are not coupled to each other. The reference solution for the rigid Earth is computed by using the satellite-determined coefficients of geopotential and the recent developments of the tide generating potential (TGP). We arrived to the conclusion that the set of terms with amplitudes exceeding the truncation level of 0.005 mas consists of 11 semidiurnal harmonics due to the influence of the TGP term u22 on the equatorial flattening of the Earth expressed by the Stokes coefficients C22, S22. There is an excellent agreement between our estimates for the rigid Earth and the amplitudes derived by Wünsch (1991). The only important difference is the term with the tidal code ν2, which seems to be overlooked in the development of Wünsch. Our amplitudes computed for an elastic Earth with liquid core appear to be in reasonable agreement with those derived by Chao et al. (1991), but the latter model was not complete. The estimated effect is superimposed on the ocean tide influences having the same frequencies but 9 to 11 times larger amplitudes. Nevertheless, its maximum peak-to-peak size is about 0.105 mas, hence definitely above the current uncertainty of UT1 determinations. Comparison with the corresponding model of prograde diurnal polar motion associated with the Earth's triaxiality (IERS Conventions, Table 5.1) shows that: 1) the two effects are of similar size, 2) there is consistency between the underlying dynamical models, parameters employed, etc. In conclusion, we recommend adding the model developed here to the set of procedures provided by the IERS Conventions.

The International Earth Rotation and Reference Systems Service (IERS) Rapid Service/Prediction Center (RS/PC) produces daily and weekly EOP combination and prediction solutions. The daily solutions are produced after 1700 UTC while the weekly EOP solutions are produced Thursday after 1700 UTC. These solutions include data from Atmospheric Angular Momentum (AAM) analysis and forecasts, Global Positioning System (GPS) solutions, Satellite Laser Ranging (SLR) solutions, and Very Long Baseline Interferometry (VLBI) solutions. The solutions are sent to roughly 700 people by e-mail per week and are picked up in roughly 40000 ftp downloads per month.

Time ephemeris is the location-independent part of the transformation formula relating two time coordinates such as TCB and TCG (Fukushima 2009). It is computed from the corresponding (space) ephemerides providing the relative motion of two spatial coordinate origins such as the motion of geocenter relative to the solar system barycenter. The time ephemerides are inevitably needed in conducting precise four dimensional coordinate transformations among various spacetime coordinate systems such as the GCRS and BCRS (Soffel et al. 2003). Also, by means of the time average operation, they are used in determining the information on scale conversion between the pair of coordinate systems, especially the difference of the general relativistic scale factor from unity such as LC. In 1995, we presented the first numerically-integrated time ephemeris, TE245, from JPL's planetary ephemeris DE245 (Fukushima 1995). It gave an estimate of LC as 1.4808268457(10) × 10−8, which was incorrect by around 2 × 10−16. This was caused by taking the wrong sign of the post-Newtonian contribution in the final summation. Four years later, we updated TE245 to TE405 associated with DE405 (Irwin and Fukushima 1999). This time the renewed vale of LC is 1.48082686741(200) × 10−8 Another four years later, by using a precise technique of time average, we improved the estimate of Newtonian part of LC for TE405 as 1.4808268559(6) × 10−8 (Harada and Fukushima 2003). This leads to the value of LC as LC = 1.48082686732(110) × 10−8. If we combine this with the constant defining the mean rate of TCG-TT, LG = 6.969290134 × 10−10 (IAU 2001), we estimate the numerical value of another general relativistic scale factor LB = 1.55051976763(110) × 10−8, which has the meaning of the mean rate of TCB-TT. The main reasons of the uncertainties are the truncation effect in time average and the uncertainty of asteroids' perturbation. As a compact realization of the time ephemeris, we prepared HF2002, a Fortran routine to compute approximate harmonic series of TE405 with the RMS error of 0.446 ns for the period 1600 to 2200 (Harada and Fukushima 2003). It is included in the IERS Convention 2003 (McCarthy and Petit 2003) and available from the IERS web site; http://tai.bipm.org/iers/conv2003/conv2003_c10.html.

We review the stability and accuracy achieved by the reference atomic time scales TAI and TT(BIPM). We show that they presently are at the level of a few 10−16 in relative value, based on the performance of primary standards, of the ensemble time scale and of the time transfer techniques. We consider how the 1 × 10−16 value could be reached or superseded and which are the present limitations to attain this goal.

We briefly summarise the planned Galileo navigation system signals and their potential application in time and frequency metrology.

The reference time scales maintained at the International Bureau of Weights and Measures (BIPM) are constructed with data from industrial clocks and primary frequency standards operated in national metrology laboratories and observatories world-wide distributed. Clocks are compared making use of techniques of time transfer between remote sites. The algorithm of calculation relies on clock weighting and clock frequency prediction. We briefly present hereafter the influence of some clocks on the scales, as well as the possibilities for improvement.

We carried out the intercomparison experiments between VLBI, GPS and DMTD to show the VLBI can measure the right time difference. We produced the artificial change using by line stretcher. At the artificial change part, VLBI and DMTD show good agreement, less than 10ps. The quantity and sense of VLBI results match well with DMTD results. Consequently, the geodetic VLBI technique can measure the right time difference.

Millisecond and binary pulsars are the most stable astronomical standards of frequency. They can be applied to solving a number of problems in astronomy and time-keeping metrology including the search for a stochastic gravitational wave background in the early universe, testing general relativity, and establishing a new time-scale. The full exploration of pulsar properties requires that proper unbiased estimates of spin and orbital parameters of the pulsar be obtained. These estimates depend essentially on the random noise components present in pulsar timing residuals. The instrumental white noise has predictable statistical properties and makes no harm for interpretation of timing observations, while the astrophysical/geophyeical low-frequency noise corrupts them, thus, reducing the quality of tests of general relativity and decreasing the stability of the pulsar time scale.

We present an analysis of glitches detected at Urumqi from 2000 to 2008. Statistics based on all known glitches, for example post glitch behavior were investigated.