We call them “the fixed stars” because they appear to be fixed, or nailed on to the celestial sphere. To the ancients, the sun, moon and planets wandered along the Zodiac, but the stars remained in one place on the dome of the sky. Relative to each other, they formed unchanging geometric patterns which were easily recognized, and memorized: the constellations. Of course, the celestial sphere itself rotated about the earth once a day, and superimposed on this motion was its revolution once a year. Today we know this is caused by the earth’s daily rotation on its axis and its yearly orbit around the sun. But the celestial sphere, the firmament, the dome of the sky, was a rigid object, with the stars fixed permanently onto the inside surface. They never moved.

Over the centuries, astronomers began to notice another motion of the celestial sphere. It was slow and oh-so-gradual, with the instruments and measurements available to naked-eye astronomy it was not possible during one man’s lifetime to see this shift. This motion seemed to affect the entire sphere itself, superimposed on its daily and yearly rotation. We call this the “precession of the equinoxes”, and it is the result of a a very slow, twenty-thousand year wobble of the earth on its axis. Although too gentle to be noticed during the lifetime of one astronomer, it still became obvious when skygazers started keeping records. The sky during the time of the Greeks was subtly different from the sky of the Egyptians and Babylonians. And they knew it, they were perfectly aware of it, although they had no clue what caused it. The stars remained fixed onto the celestial sphere, but the sphere itself, over and above its daily and yearly motion, had an additional motion to it; a very slow shift. So when you hear things like “In Dynastic Egypt the pyramids were aligned to Thuban, which was the North Star several thousand years ago”, it is the motion of the celestial sphere due to precession that they are talking about. The constellations looked the same to the Egyptians as they do to us, they were just in different places.

The rigid attachment of the stars to the dome of night was undisputed, and would remain so until the invention of the telescope, accurate mechanical timepieces, and precision measuring instruments made it possible to prove otherwise. Using these accurate devices, it became possible to determine the stars’ proper motion, their motion amongst themselves, like ants crawling very, very slowly around on the inside surface of the sphere. If you could time travel back several hundred thousand years, the sky would look very different, at least for the brighter, nearby stars.

We know today that stars are at immense distances from Earth, that they are freely suspended in three dimensional space and that they are in motion relative to one another. We also know today that the stars rotate in complex orbits around the center of the galaxy, and that most of the stars in the neighborhood of our own sun are moving along with it, like a cloud of buckshot or a swarm of bees, flying through space. We call this general, averaged-out motion the Local Standard of Rest (LSR). Its value in the Sun’s neighborhood of the Milky Way is about 240 km/sec, relative to the nucleus of the Galaxy.

But there is also an individual motion of each star, relative to the celestial sphere itself. This is the star’s proper motion, it is a tiny change in position, but it is real, and it can be measured. Proper motion is an angle, relative to the celestial sphere itself. Its magnitude will depend on how fast the star is moving relative to the Sun, the direction of its motion (a star moving directly towards or away from the Sun will show no proper motion), and its distance from the Sun. Stars very far from us may have a proper motion, but it may be too tiny to be measurable because their distance makes them appear stationary.

Stars have a random motion relative to the LSR, just as pellets in a shotgun load move relative to each other while they share a much faster common motion. These velocities are usually several tens of km/sec if they are drifting along with us, caught up in our general rotation about the Galaxy. There are other stars in random orbits around the galactic nucleus and intersecting the galactic plane at random angles which will appear to have much higher relative speeds, even though they may be traveling much slower than us, relative to the center of the galaxy.

Measuring proper motions involves determining a star’s position very precisely (relative to some average of the distant, background stars), then waiting a long time (years, even decades) and then measuring it again. Today, this is usually done by comparison of imagery taken years apart. It’s proper motion will be the shift in position measured as an angle on the celestial sphere. These numbers are typically very tiny; the proper motion of Barnard’s star, a dim red dwarf only 6 light years away, is about 10 seconds of arc per year. This is the largest known proper motion, but it is still a tiny number. It would take Barnard’s star 180 years to move across a patch of sky the size of the full moon. For all other stars, the proper motion is much less, and for the vast majority of stars, it is so tiny it cannot be measured at all.

Clearly, nearby stars have larger proper motions because their motion against the background is easier to measure. Also, you will note that the proper motion tells you nothing about the star’s speed relative to us unless you also know how far away it is. However, stars with large proper motions do (but not always!) tend to be closer to us, so they are the ones astronomers like to single out first for further study.

And one more thing: the proper motion is a measure of the star’s apparent motion to us across the line of sight. It tells us nothing about its motion IN the line of sight (towards or away from us). This value is called the radial velocity, and it is measured spectroscopically, using the Doppler effect. We can get a good, precise radial velocity regardless of how far away the star is, and we can derive it instantaneosuly, we don’t have to wait for decades between photographic exposures. So our knowledge of radial velocities is much better than our knowledge of proper motions.

Barnard’s star has a radial velocity of about 110 km/sec away from us, which suggests it is not part of our local drift through the spiral arm. This guy is a visitor from the galactic halo, just passing through the plane of the Milky Way at a time when we had the means to detect it. Ships that pass in the night…