Over the course of the night, stars will be seen to travel from East to West. Stop the Earth from rotating (or simply put a motor on your telescope to follow the rotation) and the stars seem to stop. Over the course of a year, however, the journey of the Earth around the Sun will lead to the stars wiggling about their position, with closer ones wiggling more than farther ones. This is the parallax effect, which can be seen simply by looking out of the window of a moving car and seeing things by the road moving across your field of view faster than things on the horizon. But remove all the terrestrial motions by taking two images at the same time of the year, but separated by several years and you may find some of the stars still move between frames. This is proper motion.
Proper motion is the actual motion of those stars compared to the position of our own Sun reflected in their apparent motions in the sky. Due to the distances involved, they are always very small, with the largest, the nearby Barnard’s star (a 9th magnitude red dwarf six light years from our Sun, the 4th closest star to it), moving 10.3 arcseconds (10.3/3600 degrees of arc, or about 190th of a Lunar angular diameter) per year. In two centuries or more that star will likely cross the sky by a distance similar to that of the angular diameter of the full Moon.
At this webpage, two photos are compared. One taken by the website owner on the 17th of March 2010 and one taken by the Palomar Observatory Sky Survey (POSS1) on the 20th March 1950. The Palomar plate shows not only the superiority of that telescope and viewing site, but also a number of field stars present on the website owner’s image. Over the course of sixty years, most of the field stars, and certainly the galaxies, have remained where they are, but a few close bright ones have shifted noticeably. The website includes a ‘blink comparator’ – an image that flashes between the new and old photos of the region.
Those nice fixed constellations up there? They’re on the move.