Round and Round (the Celestial Pole) We Go…

Readers of my pieces in this newsletter will note that, on occasion, I like to preface an article by noting that not everyone will find my chosen topic to be useful or informing, simply because some people will already be well aware of things that others won’t be—no writer can possibly write for everyone, all the time. This month’s contribution is intended for the benefit of those who might not be entirely clear as to what the term “circumpolar” means and why this concept is important for understanding the apparent motions of stars around the sky caused by Earth’s continual rotation about its axis.

Sooner or later, any attentive observer of the night sky is bound to notice that the closer any given star is to Polaris (the northern hemisphere’s Pole Star), the more circular its path around the sky will seem to be, through the passage of time. Another way to put this is to realize that the more northerly a star’s declination from the Celestial Equator is, the smaller the diameter—in angular degrees—its perceived arc of motion will be as viewed over time. The best example of this would be an unguided, time-exposed image taken by a camera on a stationary mount having the image centered on the North Celestial Pole, or NCP.

Many of you will have seen such pictures in the various astronomy magazines or perhaps in some of the books you’ve looked into. The kind of picture I’m describing will feature numerous “star trails”—elongated, semicircular images of stars of different colors and brightnesses, as opposed to the clean and sharp points and dots that stars would appear as on a guided image by a camera on a tracking mount. Imagine a large, multi-ringed bull’s-eye pattern with a tiny star trail very nearly marking dead center, but not precisely so. This is Polaris; its star trail is just a segment of a very small complete circle, most of which is not illuminated. Similarly, concentric circles of progressively larger diameter radiate outward from Polaris, each one only partially indicated by an illuminated star trail which will only be a segment of a complete circle. The lengths of these star trails will correspond to image exposure times. A two hour exposure would capture star trails approximating one-twelfth the arc of a complete circle. (24 hours divided by 2 = 12.) The shorter the exposure time, the more abbreviated in length the star trail will be.

We’re fortunate to have a reasonably bright star so closely indicating the true North Celestial Pole, an invisible, imaginary reference point on the sky to which is pointed Earth’s axis. Polaris is currently about 45 minutes of angle (0.75°) away from the actual polar point, a distance which is very gradually decreasing to the closest projected position of only 27 minutes or so by the year 2102, after which the star’s distance from the pole will widen. Sheer coincidence alone is responsible for the current placement of the 49th brightest star so close to the pole that the small displacement of 0.75° may be considered—for most practical purposes—almost negligible. The offset is so minimal, in fact, that you can align a telescope’s equatorial mounting directly at Polaris for reliable tracking on objects for visual observation and even for astrophotography, provided the exposure time is not unduly long. (I’m not a photographer or CCD imager, so I really can’t say what would constitute the upper limit for exposure time. Amateurs knowledgeable in this regard probably would agree that careful alignment on Polaris itself is sufficient without having to fine-tune the small offset to the actual pole.)

I mentioned the coincidental placement of Polaris close to the NCP, and that’s all it really is—a lucky, chance position that serves (over several centuries) as a good indicator of true north on a clear night, as well as a means of determining one’s latitude by measuring the altitude of the pole star above the northern horizon. Your latitude position north of the Equator—expressed in degrees—always exactly equals the altitude of the NCP above the north horizon. Some have trouble trying to imagine how this works, so we’ll use a “thought experiment” to clarify the concept.

Start by picturing yourself as being located directly on the Equator. The Celestial Equator—projected outward as a circular reference plane on the sky—is the astronomical counterpart to the terrestrial equator. We have a geocentric (Earth-centered) system for assigning precise positions on the sky for stars or other objects; this excellent celestial coordinate system uses the Celestial Equator as the plane of reference from which declination on the sky is determined. The CE itself is zero degrees and divides the sky into two hemispheres, northern and southern. Anything north of the CE is assigned a positive value in degrees and minutes of declination; the reverse is true for everything south of the CE. We would therefore identify the NCP as +90° and the opposing SCP as –90° of declination—the two polar points are 180° apart, half of a great circle running due north through due south. Unlike Right Ascension (east/west) coordinates, which are time-based and are the celestial counterpart of earthly longitude, declination values represent actual degrees of angle on the sky. For example, the declination of Arcturus is +19°11’. This star’s position north of the CE is, in degrees and minutes of angle, equal to that value, which is how far north Arcturus “declines” from the zero degree reference plane of the CE.

An observer on the Equator would have the CE passing directly overhead, right through his or her zenith point above. The two celestial poles would lie precisely at the northern and southern horizons, each having an altitude of zero degrees. All stars, regardless of declination, would be seen to rise and set at opposing east/west points. The greater a given star’s declination value north or south of the CE, the smaller in diameter its perceived arc of apparent motion across the sky would be, through time. (Just look at the parallels of latitude marked on a globe of Earth—you’ll see what I mean.) It would be impossible for any star to be seen as “circumpolar”—none would circle around either pole, because neither of the two celestial poles would technically have any altitude in the sky.

Polaris itself would actually rise and set through a tiny arc due to its offset from the true NCP; it could only be glimpsed at or near its culmination, or passage across the Celestial Meridian, the imaginary line running due north/south that connects the two polar points and cuts across an observer’s zenith, the exact overhead point for each particular observer. (A friend standing just 100 feet in any direction away from you would actually have a slightly different personal zenith!)

Some readers could be excused for wondering what all this stuff about observing from the Equator possibly has to do with those of us who reside in this area, with our local latitude of approximately 42° north. All you have to do now is shift the equatorial concept to the north, by 42°. Polaris now stands the same number of degrees of angle above the northern horizon in altitude, the Celestial Equator is well south of our zenith, and the South Celestial Pole is situated 42° below the southern horizon and thus cannot be seen in the sky. Any star that lies within 42° of the NCP is circumpolar at our latitude, meaning it circles around Polaris in a counter-clockwise direction and neither rises nor sets at any time of day or night throughout the entire year. Such a star could, under ideal and perfect observing conditions, technically always be seen at or above the northern horizon on any night! Obviously this would be, in reality, a fantasy and must be considered only in the hypothetical sense. You’ll almost always have something obscuring your actual horizon, whether it be trees, buildings, hills, etc. Light pollution, clouds, or hazy skies also will limit such observing exercises. The concept itself is what’s important here.

We can easily figure a declination limit by which sky objects would qualify as circumpolar, at any given latitude. I’ll use 42° north latitude as a base from which to work. The NCP (very closely marked by Polaris) stands 42° of altitude above the northern horizon. The pole’s declination north of the Celestial Equator is expressed as +90°. Simply subtract 42° (the radius of circumpolarity) from 90° to arrive at a declination value of +48°. Any point on the sky having a declination between +48° to +90° is therefore circumpolar as viewed from our latitude. You’ll see stars and constellation groups gradually achieve enough altitude so as to first be seen coming up out of the northeast. As the night progresses, objects sufficiently near Polaris will display an apparent “wheeling” motion as they circle the pole counter-clockwise, rising ever higher in the sky until they transit the Meridian, then drawing lower to the horizon in the northwest. Remember: only circumpolar stars can display this circular apparent motion so dramatically. Our natural “sky clock” has its face centered on Polaris.

The more southerly-positioned stars (those having declinations south of +48°) show decidedly different arcs of motion across the sky—they all rise in the east and set in the west. Look far enough south and you’ll note how certain stars seem to rise in the southeast and climb only to a low altitude above the southern horizon, even when they culminate at their highest altitudes while crossing (transiting) the Meridian. They’ll then arc progressively lower to set in the southwest, thus displaying a much-reduced “arc of visibility” above the horizon—only a small segment of a complete circle. It all depends on what direction you’re viewing and how much time you have to note changes during the night.

One of the best and simplest ways to observe the natural sky clock in action would be to start as early as twilight will allow on a good, clear night. Winter is actually best because darkness falls early and you probably would want to squeeze this two-part observation into a convenient time of night, because six hours of time are involved. The night owls among you can still manage trying this during summer, of course. Find Polaris in the northern sky, then look to the right for any given star of sufficient brightness that will meet two criteria: 1) The star must be about the right distance from Polaris to function as the hour hand on a clock, not too close but not so distant that its circumpolar motion will not be easily noticed with respect to Polaris. 2) An imaginary line joining your star of choice to Polaris should be oriented horizontally over the horizon, such that the star could be considered as being at about three o’clock in its position of altitude. (Remember: Polaris is the center of the clock.)

Once you’ve chosen a star you know you can positively identify hours later, note the time. Just reobserve your star six hours later, which is one-quarter of a day. Presto! The star will have made one-quarter of a complete circle’s arc and now stands directly above Polaris at the twelve o’clock position. The only difference from a normal clock is the direction of motion—it’s counter-clockwise, because Earth rotates west-to-east.

I’ll devote a future article to precession, the 25,870 year period during which the “wobble” of Earth’s axis causes the celestial poles to actually move around the sky on great circles approximately 47° in total diameter. Polaris is only temporarily our North Pole Star, as others have been and will, in time, become so again. Perhaps I can include a listing of certain constellations that qualify as partial or entirely circumpolar, too. By the way, Polaris is a fairly easy double star and has a magnitude 8.8 visual companion just 18” of separation away. The primary is mag 2.0 and is a “quiet” Cepheid variable; very little change in brightness has been noted in recent years.