Well, the object is moving. It is just that the image you are seeing is the image of the object from when the light left it and finally arrived in our view.
Light travels at an amazing 186,262 miles per SECOND or 670,616,629 mph. Light takes 8 minutes to reach Earth from the Sun. The next closest star, Proxima Centauri, is 4.22 Light years away. That means the image we see of those stars is over 4 years old and that is the next closest star to us. During that time it goes about its natural movement around the galaxy.
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