The stars as seen from Earth appear fixed in the sky, but in fact all stars, including the Sun, are in constant motion relative to one another as they orbit around the Galaxy. This means that stars do not occupy fixed positions in the sky, and over time they will move relative to one another. Because of the vast distances involved, this movement appears extremely slight, but it is detectable, and is termed proper motion. 'Proper' in this sense refers to motion that derives from an object's actual motion through space, rather than orbital changes affecting the observer on Earth.
The phenomenon of proper motion was first demonstrated by Edmund Halley, who noted that, after a period of many centuries, certain stars were no longer exactly in the positions ascribed to them by ancient astronomers. The stars in question were Sirius, Arcturus and Aldebaran, all brightstars relatively close to the Sun, and each with sufficient proper motion that its movement became directly observable after a period of nearly two thousand years had elapsed.
This image shows the motion of Barnard's Star - which has the highest proper motion of any star - against the background of much more distant stars. The reticle shows its position at epoch J2000, and the blue and orange markers show previous locations of the star, demonstrating how rapidly it moves across the sky. Imagery provided by Aladin sky atlas
Measuring Proper Motion
The fact that these three stars, especially Sirius, are relatively close neighbours of the Sun is not a coincidence. Due to the operation of parallax, closer objects tend to show greater apparent motion that more distant ones, and so the nearer a star is to the Sun, the greater its proper motion across the sky is likely to be. Proper motion, therefore, does not directly measure an object's motion through space, but rather the effect of that motion as seen from Earth.
This motion is envisaged as lateral across the celestial sphere, and is measured as an angle on that sphere. Proper motion for most objects in the sky is extremely gradual, and so the typical unit of measurement is the milli-arcsecond (or mas) per year, a milli-arcsecond being a thousandth of an arcsecond or one 3,600,000th of a degree.
Because objects can show apparent movement in any direction across the sky, proper motion is strictly a vector of two values, one measured west to east (right ascension) and the other south to north (declination). These values are expressed mathematically using the Greek letter 'mu' (μ), with the right ascension component being 'mu alpha' (μα) and the declination component being 'mu delta' (μδ). The actual direction of movement is designated the 'position angle' or 'theta' (θ).
All stars - indeed, all objects in the sky - show an amount of proper motion, but as the tiny units of milli-arcseconds imply, in most cases this proper motion is extremely slight. Proper motion is much more distinctive for objects closer to the Sun, with a notable example being Barnard's Star (just six light years distant) which has the highest recorded proper motion, measured at more than ten arcseconds per year. Other nearby stars also have high proper motion values, though no others approach this extreme example.
Related Concepts
An important implication of this motion across the sky is that the precise coordinates of any given object are always changing, albeit by minuscule amounts in most cases. To address this, the concept of the standard 'epoch' comes into play, a fixed point in time to which all relevant coordinates relate. At present the standard epoch is J2000 (the year 2000 expressed on the Julian calendar). Based on this, the coordinates of (for example) as star describe its position at the beginning of the year 2000, not its exact (and continually changing) current position.
Proper motion is confined to describing the movement of a star or other body across the celestial sphere; that is, the change in its position in the sky as seen from Earth. In itself, this vector is not sufficient to describe the object's actual movement through space, because it does not include a third vital component: the object's movement toward or away from the observer. This third dimension is termed the object's radial velocity. This value is rather more difficult to assess than an object's simple location in the sky, and is typically calculated from doppler shift or parallax measurement. A positive radial velocity describes an object moving away from the observer, while a negative value indicates that the object is approaching the Sun. Calculations of proper motion and radial velocity were greatly enhanced by the data collected by the Gaia mission, which allows the courses of individual stars through the Galaxy with far greater precision than had fomerly been possible.
The stars around the Sun, like all stars in the Galaxy, are in constant motion relative to one another. The nearest star to the Sun at present is Proxima Centauri, but an analysis of stellar motions shows that the Sun will have closer neighbours in the future. The fast-moving Barnard's Star, for example, is on a trajectory that will bring it somewhat closer than Proxima, approaching within 3.77 light years in about twelve thousand years' time. At the extreme of this predictive envelope is the small orangestarGliese 710. Currently more than sixty light years from the Solar System, Gliese 710's path will eventually intersect with that of the Sun, appproaching to an estimated distance of less than a fifth of a light year, though this close encounter lies more than a million years in the future.
