Because the Earth rotates on its axis, the objects in the heavens seem to move across the sky during the day and night. Just as the Sun rises in the East and sets in the West, so do the stars, planets, nebulae and galaxies in the night sky.

"Equatorial" telescope mountings have two axes, a polar axis and a declination axis, to help compensate for the Earth's rotation and aim at objects in different parts of the sky.

The polar axis of an equatorial mount should point at the north celestial pole and the process of making this so is called "polar aligning". This means making the polar axis of the mount parallel to the Earth's axis of rotation. This greatly simplifies the tracking of a celestial object across the sky with the motion of only one axis of the telescope's mount in right ascension.

For visual work, polar alignment is not that critical. An equatorial mount can simply be set up and the polar axis roughly aligned on Polaris, the North Star.

Dobsonian telescopes and altazimuth mounts do not have to be polar aligned at all.

The newer computer controlled altazimuth mounted telescopes can track an object through built-in sophisticated mathematical calculations that are transparent to the user and move the telescope in both the altitude and azimuth. However a computer-driven altazimuth-mounted telescope cannot take long-exposure photographs without the use of an expensive and relatively rare field de-rotator.

If the polar axis of an equatorial mount is not correctly aligned with the north celestial pole, there are three types of error that result:

1. Drift in Right Ascension
2. Drift in Declination
3. Field Rotation

Drift in Right Ascension and Declination are usually corrected for in the process of guiding. However, field rotation cannot be corrected for by guiding.

If the mount is not accurately polar aligned, field rotation will result in our images. Field rotation looks like circular star trails, but they center and rotate around the guide star instead of the north star.

Field rotation is independent of focal length and imaging sensor size and depends on the length of the exposure.

Using an autoguider will not compensate for poor polar alignment!

Field rotation from improper polar alignment depends on the amount of misalignment, and on the declination of the object being imaged. The angular amount of field rotation grows larger farther away from the center of the field (or wherever the guidestar is located).

To illustrate this, think of a time exposure on a fixed tripod of star trails around the north celestial pole. The stars close to the pole create shorter arcs than stars farther away from the pole. The angular amount is the same, but the linear amount of trailing is greater farther from the center.

Rough Polar Alignment

To achieve rough polar alignment the polar axis of the mount can simply be pointed at Polaris, the North Star, which is within 3/4 degree of the true celestial pole.

During the daytime or during twilight before Polaris can be seen, the mount can easily be roughly aligned by noting the latitude and magnetic variation from true north for the observing site. The mount's polar axis elevation is simply set to the latitude of the observing site. The mount's polar axis' azimuth (its compass heading) is then aimed north, taking into account for the magnetic variation from true north for the observing site. This variation can be found on the web with the Magnetic Declination Calculator at the Natural Geophysical Data Center page, or with this Google Maps interface at Magnetic-Declination.com. For example, my observing site has a magnetic deviation of about -12° west. This means that magnetic north as indicated by a compass is about 12 degrees to the west of true north, and therefore the mount must point about 12 degrees east of where the compass needle is pointing.

Using Polaris and Kochab to find the North celestial pole which is marked by an "X" in this illustration.

When twilight deepens and it starts to get dark, you should be able to find Polaris without too much difficulty by using the pointer stars in the bowl of the Big Dipper.

Polaris shines at about 2nd magnitude, so it's relatively easy to find. Just watch out you don't accidentally align on Kochab (Beta Ursae Minoris) before it gets dark enough to see both. Kochab also shines at 2nd magnitude, the same as Polaris, and depending on the time of the night and day of the year, it can be at the exact same elevation above the horizon as Polaris and can become visible in the twilight before Polaris when it is to the east of it. More than one amateur astronomer has accidentally polar aligned on Kochab. Trust me, I've done it.

Once it's dark enough to see all of the stars in the Little Dipper, look for a magnitude 4.25 star just two degrees away from Kochab, in a line drawn from Gamma Ursae Minoris through Kochab and extended a little more than half-way the distance between Gamma and Kochab. This star is 5 Ursae Minoris.

The North celestial pole lies on a line that runs from Polaris to a spot between Kochab and 5 Ursae Minoris right now. This line moves a bit due to precession, the aberration of starlight and proper motion of Polaris. If you draw a line between Polaris and roughly Kochab, the North celestial pole is about 3/4 of a degree (45 arcminutes) away from Polaris towards Kochab.

Polar Alignment Scopes

Some mounts come with a small "polar alignment" telescope that fits inside of the right ascension axis. This scope contains a reticle that, if accurately constructed and used properly, can facilitate polar alignment. Because individual light-frame exposures with DSLR cameras rarely exceed 10 to 15 minutes, accurate enough polar alignment can usually be achieved with just these polar alignment scopes.

With very good polar alignment scopes, such as the one on the Takahashi NJP or EM200 mount, an accuracy of 2 arcminutes or better can be achieved. This is good enough for long-exposure astrophotography without having to drift align.

If an accurate polar alignment scope is not used, inexpensive and less-accurate polar alignment scopes can help speed up alignment, but "drift" aligning may also be necessary for critical long-exposure work.

Star Movement in a Equatorial Telescope

A star that is monitored at high power (200x) in a telescope in a guiding eyepiece with cross hairs most probably will not stay in one exact location in the field. There are several different reasons for this.

The star will usually seem to bump around a bit if the seeing is not that good. It can move all over the place on a very short time frame if the seeing is really bad.

Even if the seeing is excellent, the star will slowly drift from its original location. It can drift East and West due to inaccuracies in the right ascension gear and drive train that move the telescope to compensate for the Earth's rotation.

This East - West movement is normally associated with periodic error, so called because the error in drift will coincide with the period of rotation of the worm gear. If a star is carefully monitored, the star will move one way for about 1/2 of the period of the worm, and then move back the other direction until it has returned to its starting position. This movement will usually be gentle and slow, but there can be quick jerks and movements from erratic error depending on the quality of the worm, gear, and components. For excellent mounts, this periodic error can be as little as a few arcseconds. For mediocre mounts, it can be as large as several minutes of arc.

For long-exposure deep-sky astrophotography, this periodic error must be guided out - either manually by the photographer or automatically with an auto-guider.

If the mount is not polar aligned to good accuracy, there will also be a slow north or south drift of a star in declination. This movement can be used to determine which way the mount needs to be moved to make the polar alignment more accurate.

The Drift Method

In the drift method, polar aligning is accomplished by monitoring the North - South declination drift of a star at high power in the eyepiece and adjusting the polar axis of the mount based on the direction of drift.

Two corrections are necessary based on two observations: one of a star on the meridian for the azimuth of the polar axis of the mount, and one of a star near the eastern or western horizon for the elevation of the polar axis.

While monitoring the drift, any east - west movement is ignored or guided out by corrections in right ascension only. It is important that no corrections be made in any north - south declination drift because this drift will indicate which way we have to move the mount to achieve more accurate polar alignment.

When drift aligning, we only care about the north - south drift!

1. Level the Mount

   The azimuth plane of the mount does not have to be perfectly level to successfully drift align, however, it is certainly easier if the mount if made as level as possible when it is set up. If the mount is not level, any adjustments in azimuth or altitude will cause an error in the alignment of the other component.

   To prove this, let's try a thought experiment. Imagine a mount where the azimuth plane is not parallel to the ground (i.e. level). Take an extreme example to make it easy to visualize, say imagine the azimuth is perpendicular to the ground. Then any azimuth adjustment will obviously affect the altitude also. If the mount is not level, the azimuth must be somewhere between 90 degrees perpendicular to the ground and parallel to the ground. Any azimuth adjustments in this case will cause errors in altitude, just to a lesser extent than in our extreme example.

   If the mount is not level (and it almost never is perfectly level), repeated iterations of a star on the meridian and horizon should be performed until there is no drift at all for 5 or 10 minutes. However, the closer to level that it is, the less iterations will be necessary.

   For the drift method of polar alignment, it is not necessary for the declination and polar axis to be exactly at right angles. Nor does it matter where the optical axis of the scope is. The only thing that matters in correct polar alignment is that the polar axis of the mount ends up parallel to the axis of the Earth's rotation.

   
   

2. Determining Directions in the Eyepiece

   Determine R.A. or Dec. Turn off the drive to find west. Push scope north to find south.

   The directions east and west correspond to the right ascension of the mount. If you stand facing north, the stars ascend (or rise), to your right, in the east, due to the Earth's rotation about its axis. Right ascension, get it? If you move the scope in right ascension, the star will move east or west in the eyepiece.

   The directions north and south correspond to the declination of the mount. If you move the mount in declination, a star in the eyepiece will move north or south.

   When you first put the guiding eyepiece in the scope, slew it in right ascension or declination, and orient the cross hairs in those directions.

   To find directions in the eyepiece:

   • Turn off the right ascension drive, the stars drift to the west.

   • Nudge the tube in declination towards the north, and the stars move towards the south in the eyepiece.

   The directions up and down depend on the orientation of the eyepiece, your head, and the diagonal if any, and can become quite confusing. Don't worry about anything else except north - south and east - west. The orientation of the eyepiece, whether or not you use a diagonal, the total number of mirror surfaces in your scope - none of these things matter with this method of finding directions.

   
   

3. Adjust the Azimuth of the Polar Axis

   In the drift alignment method, a star, roughly at the intersection of the meridian and the celestial equator, is watched at high power in a cross-hair eyepiece. The declination drift here will indicate the mount's accuracy in its azimuth alignment.

   The meridian is an imaginary line that runs from the north point on the horizon, through the zenith overhead, to the south point of the horizon. The line of the meridian is a line of right ascension. All lines of right ascension run north - south, but only the meridian also runs through the zenith. Lines of right ascension are the equivalent of lines of longitude on a globe of the Earth.

   The celestial equator is the imaginary line that runs from east to west at a 90 degree angle to the celestial poles. For example, at 40 degrees north latitude, the celestial pole is 40 degrees above the northern horizon. The celestial equator is 90 degrees from that: on the meridian it is 130 degrees above the northern horizon and 50 degrees above the southern horizon.

   Declination corresponds to lines of latitude on a globe of the Earth. Latitude is the angular distance north or south from the equator.

   The star does not have to be exactly on the celestial equator, it can be a number of degrees, 10 or 20 or so, north of the celestial equator for this correction. Technically, drift due to polar axis misalignment in azimuth is independent of the declination of the star, but a star between the zenith and celestial equator is easiest to use for polar alignment purposes.

   Place the star so it is bisected by the Right Ascension cross hair.

   The cross hairs of the eyepiece are first aligned east-west and north-south. Slew the star at high speed with the telescope controls and rotate the eyepiece until the star's movement parallels one of the cross hairs. Then note the cardinal directions with the method described above.

   A high power will indicate any drift in a shorter amount of time than a lower power eyepiece, so the higher the magnification, the better. I use about 300x and monitor the drift for about 5 minutes.

   The star is placed on the cross hair that is aligned east-west with the right ascension of the telescope. The star's drift due to polar misalignment off this cross hair will either be north or south, and this drift is monitored.

   Note that drift in right ascension can be completely ignored. Any drift in right ascension is strictly a function of the quality of the drive of the mount and its periodic error, and not the polar alignment.

   The star should be watched for 5 - 10 minutes, but in the beginning of the process when the alignment is at its worst, it's drift will be readily apparent in a short amount of time.

   This drift in declination, either north or south in the eyepiece, will indicate which way the azimuth of the polar axis needs to be adjusted.

   Azimuth Adjustment On the meridian correction for azimuth, if the star drifts South off the cross hair, the azimuth of the polar axis is too far east. Move the azimuth of the polar axis of the mount to the West (move the entire mount counter-clockwise if looking straight down on the mount from above). If the star drifts North, the azimuth of the polar axis of the mount is too far to the west, and the mount needs to be moved so the polar axis points more to the East (move the entire mount clockwise if looking straight down on the mount from above). Re-center and monitor the drift and repeat until there is no drift at all for 5 or 10 minutes.

   If the mount is grossly out of polar alignment at the beginning of this process, it may take quite a while to zero in with enough accuracy until the star does not drift at all off the line for 5 minutes. So, be patient, and while learning drift alignment in the beginning be prepared to spend a considerable amount of time practicing and perfecting this technique.

   
   

4. Adjust the Altitude of the Polar Axis

   Now find a star about 15 - 20 degrees above the eastern horizon, somewhere between the celestial equator and 20 degrees north of it. If you have a clear horizon, you don't even have to change the declination of the telescope from what you used for the azimuth correction - simply slew it in right ascension and find a star somewhere above the eastern horizon.

   Stars too close to the horizon will be adversely affected by differential atmospheric refraction and poor seeing.

   A star on the western horizon can be used, but the directions given below must then be reversed.

   Again, align the cross hairs east-west and north-south, and place the star on the cross hair that runs east-west, and watch for its drift off the line to the north or south.

   Altitude Adjustment On the Eastern horizon correction for the altitude of the polar axis, if the star drifts south, the polar axis is too low and needs to be elevated. If the star drifts north, the polar axis is too high and needs to be lowered. Re-center and monitor the drift and repeat until there is no drift at all for 5 or 10 minutes.

   After completing the initial meridian and horizon checks, go back to the meridian and check it again.

   (Note: if the eastern and western horizons are blocked it is possible to do the altitude adjustment by drifting on a star within about 10-20 degrees of Polaris, due East or West.)

   Even with the years of experience I have with this method, it usually takes me about 30 - 45 minutes to get really good polar alignment with the drift method, even after using a polar alignment scope built for the mount that get's me pretty close to start.

   Once you become familiar with the drift method, you can gauge about how far the mount needs to be moved by how far the star drifts in a set amount of time.

Northern vs Southern Hemispheres

When the drift alignment method is used in the southern hemisphere, the direction of drift is reversed for the instructions. The shortcut would then be: N-E-L: if a star on the celestial equator drifts North for the azimuth adjustment, the mount is too far East. If a star on the Eastern horizon drifts North, the mount is too low.

Polar Alignment Can Never Be Perfect

Perfect polar alignment can never be attained because of atmospheric refraction.

When we look out through the Earth's atmosphere, we are essentially looking through a wedge that slightly shifts the position of stars depending on their elevation above the horizon. When we look near the horizon we look through more of the Earth's atmosphere than when we look directly overhead. This is why we can sometimes look directly at the setting Sun, most of its light gets filtered by the thick atmosphere. This wedge effect of the atmosphere, called atmospheric refraction, also causes the apparent position of objects viewed through it to shift. For example, when an object is just above the horizon, it's position is shifted upwards by atmospheric refraction. In fact, when we see the Sun exactly on the horizon, it is actually below it, but the light is being bent upwards and over the horizon by the atmosphere, so we can see it.

This also means that the true position of every star in the sky is slightly different from where we see it. Stars closer to the horizon are shifted more. Because of this effect of "differential atmospheric refraction", the apparent position of the refracted celestial pole will change, both in altitude and azimuth, depending on the star being observed.

Brad Wallis and Robert Provin pointed this effect out in A Manual of Advanced Celestial Photography. About it they said "Thus, 'perfect polar alignment is an illusion, and to pursue it is to chase an apparition."