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A polar aligned equatorial mount allows a telescope to accurately track the movement of celestial objects across the sky.  While this is mandatory for photography, it's benefits should not be overlooked for visual observation as well.  I must admit to being an equatorial mount advocate.  My own observing interests lie primarily in lunar and planetary observation.  This class of observation is also greatly aided by a polar aligned telescope.  When you can relax at the eyepiece and wait out the few precious moments of great seeing without worrying about tracking and making image position adjustments, the thrill of planetary observing becomes obvious.  At public star parties, you also don't have to keep readjusting the telescope and can be sure that the object you are explaining to your current visitor is still visible.

When used for visual use, the telescope may be roughly aligned on the celestial pole.  The degree of error you choose to accept is directly related to how often you are willing to center the object being observed as it drifts out of the field of view.  For high magnification planetary viewing, the more accurate the alignment the better.  Still, you need not spend ten to twenty minutes doing the classical "drift alignment" procedure.  You can get pretty close in just five minutes or so using the method presented here.  (The times I speak of are assumed to be for the average telescope user who is not being timed for the world record.  I am sure there a some folks who can drift align a telescope to within a few arc seconds of the pole in only a few minutes.  If you can already do that, this procedure will not help you improve your speed or accuracy.)

Most manuals that come with a telescope explain an alignment method.  It often starts with a statement to use the declination setting circle to point the telescope to 90°.  What if your setting circles are not accurately set in the first place? Your alignment will suffer by the amount of the error.  The procedure described here will allow you to correct that condition also without depending on the initial setting circle accuracy.

Aligning on Polaris:
        The steps for a basic polar alignment will first get the telescope pointed towards Polaris.  After this is completed, you may stop if casual visual observation for a short time is your goal.  If you are setting up for a longer session or will be doing some serious high magnification viewing or sketching, then you will want to follow the second half of the procedure and offset the alignment from Polaris to the celestial pole.  If you will be doing photographic work, this procedure will get you more than close enough to begin a drift alignment session.

1. The first step in the polar alignment procedure is to set up the telescope's tripod or base approximately level.  Extreme accuracy is not required here.  The only purpose for even roughly leveling the base is that it ensures that when you make altitude or azimuth changes to the polar axis later during alignment, they do not significantly interact.  You need only be level enough that an altitude change does not make much of an azimuth change at the same time.
    
     This point is often over emphasized.  Only for "GO-TO" altazimuth telescopes is accurate leveling often required.  In that case, the leveling is part of the assumed algorithm for allowing the telescope's control computer to deduce where it is initially pointed.  The important point for a non-GO-TO equatorial mount is that the polar axis be pointing exactly to the celestial pole.  So long as this requirement is met, the leveling of the base is immaterial.  You could bolt the tripod head to a nearby wall if you wanted to just so the RA axis is aligned with the pole.  An approximate level of the base does help in getting the polar axis aligned.  Only because of that do we want to start roughly level.
    
2. In order to align the polar axis to Polaris, start with the declination axis of the telescope parallel to the horizon.  Set the right ascension lock in this position.  In this position, the telescope tube can swing up and down in altitude about the declination axis.  Set the tube to 90° as shown on the declination setting circle.  Don't worry too much about the setting circle's accuracy at this point.  Now, move the whole telescope wedge or base in azimuth and bring Polaris into the center of the finder and then a low power eyepiece.  You will probably need to adjust the declination setting up or down slightly as you turn the wedge or base side to side to do this.  Once Polaris is centered, lock the telescope mount's azimuth adjustment control in this position.  Also set the declination lock at this time.
    
     At this point, the polar axis is pointed "north" or at least to the azimuth position of Polaris.  As the telescope tube is swung up and down about the declination axis, Polaris will pass through the center of the field of view.  Adjust the telescope until Polaris is visible in the center of the eyepiece.
    
3. Next, you need to adjust the telescope's polar axis so that is points to the altitude of Polaris.  To do this, leave the declination axis locked and rotate the telescope about the right ascension axis 6 hours (90°.) Now the declination axis of the telescope is is pointed in a vertical plane toward the meridian.  Don't unlock the declination just yet, but note that the tube would swing left and right with the telescope oriented in this position.
    
     Now loosen the the altitude adjustment for the telescope's wedge or base.  Adjust the altitude of the telescope until Polaris is visible in the center of the finder and eyepiece.  You will now have to loosen the declination lock and make slight adjustments to get Polaris centered.  This adjustment is made necessary because the initial altitude (latitude) setting of the base was not yet set up, the telescope's base may not have been exactly level, and the declination and right ascension axes may not be exactly perpendicular.
    
4. As a final fine adjustment, center Polaris in the eyepiece, lock the declination axis and unlock the right ascension axis.  Rotate the telescope 12 hours (180°) in right ascension.  Check to see if Polaris is still centered in the field of view.  If it is not, use the declination axis slow motion control to bring Polaris half way to the center then adjust the azimuth control on the base or wedge to move polaris the remaining distance to the center.

With the declination axis locked, you may now adjust your declination setting circle to read exactly 90° as the tube should be parallel to the polar axis.  You may want to try rotating the telescope in right ascension while watching the position of Polaris in the eyepiece.  If it moves from the center of the field of view, then the alignment is still a bit off.  If the base of the telescope is substantially off level, you may need to go back to step 1 to check everything.  If, after a second iteration, the alignment is still not good, it is possible that the two axis of the telescope are not exactly perpendicular.  The amount of this error will be one half the distance Polaris moves in the eyepiece.

You should be very close at this point.  You may stop now if you will be doing only casual visual observation.  The telescope should track objects for 20 minutes or so without need for much re-centering.  If you will be doing extended observation or sketching, you can improve the tracking by continuing the procedure and offsetting the telescope to the actual celestial pole rather than Polaris.  This will also substantially help the positioning accuracy of digital or regular setting circles if you plan to use them to aid you in locating faint objects.

Offsetting to the celestial pole:
        The final portion of this alignment procedure is to move the telescope polar axis so that it points to the celestial pole rather than Polaris.

More to come...