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.
With a single object, there’s no real way to know. However, there is a trend that points in this direction when you look at all of the objects in the sky.
As a general rule, everything is moving away from us. Additionally, the farther something is from us, the faster it is moving, and the speed with which things are moving away from us is directly correlated with the distance.
This leaves us with two options. Either Earth is literally the center of the entire universe and we are super duper extra special, or we aren’t and something else is going on. And if you take the position that we are average and not literally the center of the universe and then try to model what is going on, it turns out that what we see in the sky maps very accurately onto the metric expansion of space.
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