Methods of classical mechanics and astrometry are shown to be sufficient for deriving the exact mathematical formulae necessary for the solution of the problems of astrometry and connected to it sciences. From exact formulae it is not difficult to proceed to formulae of any approximation required by practice. Incompatibility of principles of the SRT and GRT with the principles of classical mechanics is shown and the question is raised of validity of the opinion submitted in academic magazine «Common sense», according to which the relativistic mechanics might be considered as more precise than mechanics of Newton [13. V. 1. P. 12].