  We investigate the time evolution of the redshift of the spectrum of
electromagnetic radiation that is emitted by the star that moves in the
vicinity of supermassive black hole. For the case of Schwarzschild black hole
we solve this problem exactly in General Theory of Relativity. Also we
formulate an approach that gives possibilities to solve the inverse problem:
reconstruction of motion of a star in the vicinity of black hole using the
redshift data. This approach consists of two steps. The first step gives
possibilities to find unique solution for the integrals of motion of the star
by solution of a system of non-linear equations, rather than the direct
application of standard statistical methods. For this purpose we consider
properties of congruences of isotropic geodesics that connect of the worldline
of the source and the worldline of the observer. The second step is the
application of standard least squares method in order to obtain more accurate
solution. This approach is used on the numerical model of the star in the
vicinity of the Center of our Galaxy.
