  We investigate the astrometric performance of the FORS1 and FORS2 cameras of
the VLT at long time scales with emphasis on systematic errors which normally
prevent attainning a precision better than 1mas. The study is based on multi-
epoch time series of observations of a single sky region imaged with a time
spacing of 2-6 years at FORS1 and 1-5 months at FORS2. We performed a detailed
analysis of a random error of positions that was shown to be dominated by the
uncertainty of the star photocenter determination. The component of the random
error corresponding to image motion was found to be caused primarily by optical
aberrations and variations of atmospheric PSF size but not by the effect of
atmospheric image motion. Comparison of observed and model annual/monthly epoch
average positions yielded estimates of systematic errors for which temporal
properties and distribution in the CCD plane are given. At frame center, the
systematic component is about 25 mu-as. Systematic errors are shown to be
caused mainly by a combined effect of the image asymmetry and seeing variations
which therefore should be strongly limited to avoid generating random and
systematic errors. For a series of 30 images, we demonstrated presicion of
about 50 mu-as stable on daily, monthly, and annual time scales. Relative
proper motion and trigonometric parallaxes of stars in the center of the test
field were derived with a precision of 20 mu-as/yr and 40 mu-as for 17-19 mag
stars.
