Is modern astronomy capable of telling us where is the center of the universe?
No, because it’s believed that there is no center of the Universe. In general, all galaxies are moving away from each other, and this would not be true if there were a center. Instead, the Universe is thought to be expanding in all dimensions, causing the space between (and within) galaxies to expand, apart from the actual movement in space of the galaxies themselves. It’s a somewhat difficult idea to grasp initially.