  The work is devoted to the critical analysis of theoretical prediction and
astronomical observation of GR effects, first of all, the Mercury's perihelion
advance. In the first part, the methodological issues of observations are
discussed including a practice of observations, a method of recognizing the
relativistic properties of the effect and recovering it from bulk of raw data,
a parametric observational model, and finally, methods of assessment of the
effect value and statistical level of confidence. In the second part, the
Mercury's perihelion advance and other theoretical problems are discussed in
relationship with the GR physical foundations. Controversies in literature
devoted to the GR tests are analyzed. The unified GR approach to particles and
photons is discussed with the emphasis on the GR classical tests. Finally, the
alternative theory of relativistic effect treatment is presented.
