ESA (European Space Agency) put up a satellite a few years ago to map all the stars in the sky, well, the brightest million or so anyway. Not all the stars are fixed to the firmament, some of them, like Barnard's star are wandering around loose. You would have be pretty persnickety to tell, but the robot satellite Hipparcos and Dennis di Cicco, astronomer extraordinaire, managed to do so. The jaggy line running up the center of the diagram is the star's path according to Hipparcos. The round black spots are M. di Cicco's observations. Notice that the period of time covered is about two years while the change in position is about 18 arc-seconds. At an arm's length from your eye that is about 3/1000th's of an inch, or about the thickness of a sheet of 20 pound paper. Not very freaking much. It took two years to travel that far and it's traveling somewhere around 100 miles per second. Compare that to the 5 miles per second you need to reach low Earth orbit.
Barnard's Star is about 6 light years from Earth, which makes it one of the closest stars and also makes it's motion detectable.
2 hours ago