The “parsec” is, of course, a unit of distance, not one of time. The word is short for “PARallax-SECond”, or the distance at which a star has a parallax of one second of arc (a sixtieth of a sixtieth of a degree). One parsec is equal to about 3.26 light years.

Astronomers can measure fairly accurately the distance to nearby stars by triangulation, they photograph a star at opposite ends of earth’s orbit (six months apart) and notice how the star appears to shift position against a background of much more distant stars due to parallax. Another example of parallax is the shift in position of a close object (say, a shrub in your yard) against a backgound of the houses across the street when you look at it by alternately blinking your eyes. The distance between your eyes is the “base line” and we use parallax subconsciously to judge distances to nearby objects.

For more distant objects, parallax doesn’t work because the shift is too small. You have to increase the baseline to use parallax to derive a disatance geometrically. And the largest baseline possible is the earth’s orbit itself, a radius of 93,000,000 miles, or 1 Astronomical Unit. A star 1 parsec away will seem to shift back and forth 1 second of arc against the background of more distant field stars on two photographic images taken six months apart. The parallax shift of a star is the size of an Astronomical Unit viewed at the distance to the star.

A handy consequence of this definition is that the distance (in parsecs) of a star is simply the reciprocal of its parallax. So a star 2 parsecs distant will have a parallax of a 0.5″. A star with a parallax of 0.01″ will be a 100 parsecs away. As it turns out, there are no other stars within a parsec of of our own solar system, so all parallaxes are under a second of arc. Alpha Centauri, at 1.29 parsecs, has a parallax of 0.776″.

The reason for this rather awkward system of nomenclature is that the parallax of stars is one of the few stellar properties that can be measured directly. The first star’s distance to be actually detrermined in this way was 61 Cygni, by Bessel, in 1838. It used to be done with precision surveying instruments with exotic names like filar micrometers, zenith tubes or meridian circles, and then it was put on a mass production basis with photography. Take two photographs a few months apart, and the nearby stars’ images will shift back and forth when observed on the photographic plate under a powerful microscope. The more distant, background stars, shift too, but their shift is too small to be measurable. They form the coordinate system against which the parallax shift is described. Careful measurement of stellar images on photographic plates allowed for large numbers of parallaxes to be quickly catalogued. But it wasn’t until 1838 that we had even the remotest idea of the scale of even the nearby stellar neighborhood. 61 Cygni has a parallax 0.286″, corresponding to about 3.5 parsecs. I often wonder what Bessel felt when, after checking and double checking his calculations, he finally realized how really far away even this relatively nearby star was. It must have been really mind-blowing, to realize we finally had a way to measure the heavens, and he was the first to have any idea just how big the universe was. How Bessel knew 61 Cygni was “nearby” I will discuss below.

Galileo tried to measure stellar parallax in the 1600s but his equipment was too primitive for the job. Today, the term “parallax” is often used synonymously for “distance”, even if the distance is estimated with some totally different method. You hear terms like “spectroscopic parallax” (a distance estimate based on our assumptions about the structure and luminosity of stars) or “secular parallax” a trigonometric baseline based on the sun’s orbit around the galaxy.

Trigonometric parallaxes were only good for distances of about a hundred light years (it is extremely difficult to measure very tiny angles!). Today, satellite telescopes like Tyco and Hipparchos have improved the art considerably, but it is still very hard, and useful only for nearby stars. But all distances in astronomy are measured indirectly except for parallaxes. These are the only objects for which we can derive an assumption-free, geometrical distance. The rest of the astronomical distance scale is calibrated using these few thousand direct measurements, its an inverted pyramid of guesswork that is overhauled every time a slightly better system of measuring parallaxes is devised.

So how did Bessel know 61 Cygni was probably fairly close to earth and a good candidate for his new method? 61 Cygni was one of a handful of stars known to have a large proper motion. Proper motion is the angular motion of a star across the distant stellar background due to its own motion through space. The stars are not glued to the celestial sphere, they are all in motion, and although these proper motions are small, they are measurable, and they are typically much larger than parallaxes and therefore much easier to measure.. You will recall that the largest parallax is under a second of arc, but the largest known proper motion (Barnard’s Star) is 12″ per year! 61 Cygni, also known as Piazzi’s Flying Star, has a proper motion of 5″/yr. Bessel was right to deduce it was probably nearby, since the closest stars could be expected to have fairly large proper motions. Of course, it wasn’t a sure thing. Proper motion does not only depend on how fast the star is moving, but on how close it is, and whether is motion is radial or perpedicular to our line of sight. A star with no proper motion could be either very far away and its motion undetectable, or it could be travelling toward or away from us, or parallel to us. Still, as a general rule, a high proper motion generally means a relatively nearby star.

There are some other terms you may stumble across if you are researching these matters. The first is “aberration of light”. This is an effect on a star’s position caused by the earth’s motion through space. It causes the apparent location of the star to shift forward in the direction of earth’s motion. It is the same effect you see when a vertically falling rain appears to be coming from ahead of you when in a moving car: the drops seem to be flying towards your windshield not just falling from directly above. The effect is small, less than 20″, but it must be corrected for. The other effect is nutation, a small, short term sinsoidal variation in the coordinate shift caused be precession of the equinoxes. Its cause is slight variations it the direction of earth’s axis on the celestial sphere caused by periodic variations on the moon’s orbit. It has to be corrected for as well.