  We derive the astrometric orbit of the photo-center of the close pair alpha
UMi AP (=alpha UMi Aa) of the Polaris multiple stellar system. The orbit is
based on the spectroscopic orbit of the Cepheid alpha UMi A (orbital period of
AP: 29.59 years), and on the difference Delta mu between the
quasi-instantaneously measured HIPPARCOS proper motion of Polaris and the
long-term-averaged proper motion given by the FK5. There remains an ambiguity
in the inclination i of the orbit, since Delta mu cannot distinguish between a
prograde orbit (i=50.1 deg) and a retrograde one (i=130.2 deg). Available
photographic observations of Polaris favour strongly the retrograde orbit. For
the semi-major axis of the photo-center of AP we find about 29 milliarcsec
(mas). For the component P, we estimate a mass of 1.5 solar masses and a
magnitude difference with respect to the Cepheid of 6.5 mag. The present
separation between A and P should be about 160 mas. We obtain the proper motion
of the center-of-mass of alpha UMi AP with a mean error of about 0.45 mas/year.
Using the derived astrometric orbit, we find the position of the center-of-mass
at the epoch 1991.31 with an accuracy of about 3.0 mas. Our ephemerides for the
orbital correction, required for going from the position of the center-of-mass
to the instantaneous position of the photo-center of AP at an arbitrary epoch,
have a typical uncertainty of 5 mas. For epochs which differ from the HIPPARCOS
epoch by more than a few years, a prediction for the actual position of Polaris
based on our results should be significantly more accurate than using the
HIPPARCOS data in a linear prediction, since the HIPPARCOS proper motion
contains the instantaneous orbital motion of about 4.9 mas/year = 3.1 km/s.
Finally we derive the galactic space motion of Polaris.
