There are many factors that enter into predicting the position of a star from the ground at this level of accuracy. Most commercially available software will not work. There are many effects that have to be accounted for:

Position of the star Precession of earth axis Nutation of earth axis Chandler Wobble of earth axis Stellar Aberration Proper Motion of Polaris Location of observer on earth Time of observation Atmospheric refraction General relativistic effects

** Location of Star** First, you have to obtain the Right Ascension and Declination of Polaris
computed for a reference epoch. The Smithsonian Astrophysical Observatory
star catalog gives star positions only to an accuracy of +/- 0.8
arcseconds which is not adequate. The Hubble Guide Star Catalog gives
star positions to an accuracy of +/- 0.5 arcseconds which is slightly better
but still not good enough for any one specific star such as Polaris.
The 1996 edition of the
US Nautical Almanac available from the
US Naval Observatory, lists the position of Polaris to a precision of
about 6 arcseconds using the FK4 astrometric system developed for epoch 1930.0
and presessed to the current date.

The
'FK5 Catalog' lists the computed positions for some 5000 stars to an
accuracy of +/- 0.02 arcseconds which is in the right ball park. This
catalog is an enhanced version of the FK4 astrometric reference catalog
created for epoch 1930, but including a much more sophisticated model of
the earth's motion. The *Hipparcos Input Catalog*, which is based on the FK5
positions, gives the J2000.0 position
of Polaris to an accuracy of 0.03 arcseconds as: RA = 2h 31m 48.704s and
Dec = +89d 15' 50.72" and indicates a proper motion of: 15mu(ra)cos(dec) = +0.038
arcseconds/year and mu(dec) = -0.026 arcseconds/year. The yearly publication
* Apparent Places of the Stars* for 1996 is also based on FK5 and gives
the position of Polaris on February 8, 1996 as: RA = 2h 28m 0.61s, Dec = +89d
15' 5.49". Positions are given every day of the year and include aberration,
precession and major long term nutation corrections.

** Proper motion** The next correction is for the
proper motion of Polaris which is
about 0.046 arcseconds per year from the Standard Astrometric Epoch of your
table. Once you have added this, it is such a small increment that
you do not have to recompute it for a few years. We will ignore it here.

** Relativistic effects** You might also consider adding a correction to account for the fact that
we are sitting at the bottom of a gravitational well, and that incoming
light rays will be slightly bent. For Polaris, at sea level, this amounts to
only about 0.002 arcseconds or so, and you can ignore it. For astrometric
satellites such as Hipparcos, however, this effect has to be added.

** Precession** Next, you have to correct this position for the precession of the
earth to translate it from the date of the catalog position, to the
date when you made the observation.
This amounts to about 10 arcseconds per year for Polaris as the
earth's polar axis moves along a 25,800 year circle in the sky with a diameter of
some 47 degrees.

** Chandler Wobble** Then there is the correction for the wobble of the earth's axis, known as
the Chandler Wobble, the amplitude of which can vary from 0.1 to as much as
0.7 arcseconds. The earth is not a perfect sphere, but slightly flattened,
and it rotates about a slightly different axis than the mean figure of
the earth. Also, earthquakes cause mass near the
surface to get moved around which changes the moment of inertia of the earth.
These effects cause the direction of the pole to trace a roughly
circular path about the nominal north pole direction on a roughly 14 month
(428 day) basis, however the mean amplitude varies in a very complex
pattern from cycle to cycle.

** Nutation** An even slower effect is the nutation of the polar axis on a roughly 19 year
cycle due to the changing lunar gravitational attractions upon the earth's
equatorial bulge. There are several components to this effect.
The Lunar component amplitude is +/-9 arcseconds towards the ecliptic
pole with a period of 18.6 years. The solar component is +/- 1.2 arcseconds
over 0.5 years; There is a 'fortnightly nutation' of +/- 0.1 arcseconds per
5 days; there is also a seasonal variation caused by the movement of
airmasses of +/- 0.18 arcseconds per year.

** Observer location** Next, you need to know your latitude and longitude on the earth to
an accuracy better than one second of arc which, given the earth's polar
radius of 6356.779 kilometers, requires a positional accuracy of
less than 30 meters. This is available from USGS topological maps of the
viewing location, or from the Global Positioning System of satellites, with
the help of a transponder. You can practically buy this at Radio Shack!

** Local time** Next, you have to determine where on its diurnal circuit around the north
celestial pole it is. Polaris moves in a circle about 1 degree in radius
every 24 hours which is 1 arcsecond every 8 seconds of clock time. This means
you need fairly precise timekeeping using the WWV timesignals. The
local time is then converted into Universal Time, and from the time of the
year and the longitude of the observer, you determine the Local Sidereal
Time which tells you which Right Ascension is on the north-south meridian
at the time of the observation. For this you need to know the observing date
to convert from Ut to Local Sidereal Time.

Next, you use the Right Ascension, Declination for the date of the observation, together with the Local Sidereal Time, to compute a first approximation to Polaris's Azimuth and Elevation. This is a trivial computation using two simple trigonometric formulae.

** Atmospheric refraction** Now, you have to correct the elevation angle for atmospheric refraction
which for sightings of Polaris at elevation angles below 80 degrees will
exceed 1 arcsecond. This correction, however, only affects the elevation angle
and not the azimuth angle so in principle we don't need to worry about it if
we only want azimuth angles. It makes the elevation of the star look
higher than it actually is. Unless you are an eskimo, most observations
are made at earth latitudes near 30 - 40 degrees so that Polaris will be
at elevation angles between 30 - 40 degrees where atmospheric refraction will
easily exceed 1 arcsecond. There are standard formulae which can make
this correction, but it changes with atmospheric humidity and pressure.

** Stellar aberration** The next correction we have to make is for stellar aberration. Because
the earth moves at about 30 kilometers per second in its orbit, star images
make a 20 arcsecond loop about their true positions in the sky. The geometry
of this effect is that stars near the North and south poles of the earth's
orbit in the ecliptic plane execute circular motions, and stars in the plane
of the ecliptic move from side to side along the ecliptic plane. We
need to compute the ecliptic coordinates of Polaris, and from the date of
the observation, determine which direction the offset due to aberration
will be from the astrometrically determined positions of Polaris's TRUE
position.
In principle, if the observations are made from an earth satellite, a
similar effect will be present at a level of 5 arcseconds for
satellites with orbital velocities of 8 kilometers/sec. Under these
conditions, of course, no
correction is needed for atmospheric refraction!

Once we have determined the true Right Ascension and Declination of Polaris at the moment of observation, and have added corrections for aberration and atmospheric refraction. we now have the APPARENT position of Polaris for the day, date and time of the observation, and from a specific earth latitude and longitude. All these steps are relatively straight forward and can even be represented by a mathematical formula, but there would be several steps needed to do the calculation. Any table would be VERY lengthy because it would have to have 8 seconds in time resolution for every day of the year, for every 30 meters on the surface of the earth! Each year there would be a new table to account for the new nutation constants and the conversion of UT to Local Sidereal Time.