When the light first left the galaxy in question, the Earth was much closer to where that galaxy was than it is now as the light is arriving from where it was 10 billion years ago and the universe was much younger and smaller then. Meanwhile that galaxy has moved much further away over the 10 billion years it has taken the light from it to reach our current position as the universe continues to grow at an accelerated rate of expansion. If we were now to send a beam of light in the apparent direction of the galaxy it will probably never reach it since the rate of the expansion of the universe now exceeds the velocity at which light travels toward it and even if it finally did reach that far the galaxy has probably moved so that it is no longer in the same direction it is now observed.
Although the age of our current universe is estimated to be less than 14 billion years old the current size of the universe is many times the distance light traveled during this time and continues to expand at an accelerating rate. Some estimates of the current size of the universe range from 156 billion light years to much much more. This means that all but a small fraction of the universe is now beyond our field of view.
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