I’ve made a Powerpoint Animation (and the above animated gif, click to see it move) that demonstrate stellar proper motion. Note that the animation is quite complex, and can only run for about 20 seconds before the various layers stop moving.
Proper* Motion is the apparent angular motion of stars across the sky, due to their orbits around the center of the Milky Way Galaxy. Lacking any depth perception (but see my post about parallax), astronomers have to use different techniques to measure a star’s radial (directly toward or away from us) and transverse (across the sky) motions. Proper motion is that transverse motion.
This animated gif shows the proper motion of Proxima Centauri (alpha Centauri C) taken from 2000-2010. The images are actual research data taken by the RECONS group with the 0.9m (36-inch) telescope at the Cerro Tololo Inter-american Observatory in Chile, with a cadence (for the gif, anyway) of about 6 months between each frame. For a star, Proxima Centauri moves pretty fast, but even at a rate of 3.8″/year, it only covers 1/50 of the angular width of the full moon in 10 years. Planets and asteroids can move that far in a day.
Historically, proper motions (the transverse motion) have been used to find potential nearby stars. The idea is that the stars that appear to be moving the fastest should be the closest. Consider the powerpoint animation: your brain wants to put the slow-moving stars in the background, and the fast moving ones closer**. It’s not perfect, of course; every star is actually on its own unique orbit around the center of the Milky Way Galaxy. Proxima Centauri, the closest star, has only the 17th highest proper motion in the NLTT catalog; Barnard’s Star, the fastest-moving star, is the second-closest star system. Still, the 3.8″/yr motion of alpha Centauri AB (Proxima was unknown until 1915) combined with its brightness- combined, they are the fourth-brightest point of light in the sky- was enough to single it out to 17th century astronomers as a potential nearby star worthy of measuring a parallax to.
*In this case, we’re using an alternative definition of the word “proper” that means “unique” or “intrinsic to the object”, rather than the normal definition, where “proper” = “appropriate”. Oh, jargon.
**Technically, that effect is called motion parallax- angular shifts due to YOU moving in a straight line (as opposed to the annual parallax of stars caused by the Earth orbiting the Sun, as I talked about here). The powerpoint animation is a “parallax scroller”, where multiple layers scrolling at different speeds produce that illusion of depth; I used four and then several individually-moving stars on top of that. Old console games like Donkey Kong Country used parallax scrollers to fake 3D environments they weren’t actually capable of.