An analytical formula for the time transformation TDB-TDT valid over a few thousand years around J2000 has been computed with an accuracy at the 1 ns level. This computation was carried out by integrating the differential equation derived from a general metric.
The transformation TDB-TDT is independent of the PPN parameters, γ and β, and of the 3 most commonly-used coordinate systems (standard, isotropic, Painlevé), at least at the 1 ns level.
The analytical theories ELP2000 and VSOP82 developped at the Bureau des Longitudes were used for the motions pf the solar systém bodies, Furthermore, the numerical procedures described by Hellings and Davis to calculate this transformation yield different results to our own procedure. These differences are due to the long-period terms of the planetary theories which are averaged out
in the numerical procedures. These terms are generated by resonances in the Solar System.
On the example of Ostrów Tumski in Wrocław (Silesia, Polish lands) an attempt of identification of places associated with trade and exchange in early medieval strongholds was made. The alleged marketplace existed in the stronghold from the end of the 11th century to the end of the 12th century. Its existence would be confirmed by the empty square between buildings, the accumulation of finds related to trade and exchange as well as spending free time. The connection of some buildings form Ostrów Tumski with commercial activities is also not excluded. On the basis of analogies from the main centers of the Piast state and selected sites from the Bohemian and Moravian territories, the potential location of the marketplaces was analyzed. Attention was drawn to the relationship between finds related to trade and exchange with other manifestations of economic activity (e.g. non-ferrous metallurgy). An attempt was also made to answer the question when and in what political and economic conditions such places could be created.
An algorithm for correction of two-axes laser mount direction and gates in case of atmospheric drag induces diviations from the predicted satellite motion is described. Results of numerical simulations are shown.
We tried to determine as accurately as possible the geocentric coordinates of the Hvar Doppler station in the coordinate system of broadcast and in one of precise ephemerides, on the basis of Doppler observations from the project IDOC-82 and of broadcast ephemerides alone. With this aim in view it was necessary in the first place to calculate for the project IDOC-82 two new variations of multipoint solutions by means of broadcast ephemerides (MPBE), taking into account 11 stations, i.e. 10 suitable stations. Coordinates X, Y, Z for the Hvar station contained in this way were thereupon converted from BE-system by means of
three-dimensional Helmert transformation and by using available identical stations from previous projects EDOC-2, ERIDOC and ALGEDOP-82 for all of which multipoint solutions with precise ephemerides (MPPE) are dsposable.
An analytical method od determination of luni-solat perturbations of the satellite motion is described here. The motion of perturbing body is described by trigonometrical series with the necessary accuracy. The determination of perturbations is made by numerous analytical transformations of the series by means of computer. As a result of these transformations the original accuracy is lost because of the limitation of the number of terms in series. The loss of accuracy is subjected to analysis by means of numerical tests and intotal accuracy of original series is estimated for fixed required accuracy of the calcualtion of satellite coordinates.