The average star in our Galaxy moves at a speed of about 10 kilometers per second or, in terms of kilometers per hour, at a speed of about 36,000 kilometers per hour. This speed seems high and so we must consider whether we can see this motion or not.

Because of the large distances to stars, the predicted motion is small. Is it so small that we can't detect it?

Well, in one hour, the star moves a distance of 36,000 kilometers, at most. If the closest star, Proxima Centauri, moved at this speed, would we be able to see the motion? To figure this out, note that the distance to Proxima Centauri is about 4.25 light years (a light year is the distance travels in 1 year, 1 light year is 5.9 trillion miles or 9.5 trillion kilometers) = 25.3 trillion miles or around 40.2 trillion kilometers. The angular distance it moves in one hour is around 0.00000002 degrees! or around one-millionth of one arc second (1 degree = 60 arc minutes and 1 arc minute = 60 arc seconds). We must wait over 1 century in order to see Proxima Centauri move 1 arc second or 1/3600-th of a degree. Even after 1 century, such tiny motions are not detectable with the unaided human eye. The smallest angle the human can measure is around 1 hundredth of a degree or around 0.5 arc minutes.

Stars appear to be fairly stationary on the sky because of their exceedingly large distances.