  In this paper we examine the possibility of testing the equivalence
principle, in its weak form, by analyzing the orbital motion of a pair of
artificial satellites of different composition moving along orbits of identical
shape and size in the gravitational field of Earth. It turns out that the
obtainable level of accuracy is, realistically, of the order of 10^-10 or
slightly better. It is limited mainly by the fact that, due to the unavoidable
orbital injection errors, it would not be possible to insert the satellites in
orbits with exactly the same radius and that such difference could be known
only with a finite precision. The present-day level of accuracy, obtained with
torsion balance Earth-based measurements and the analysis of Earth-Moon motion
in the gravitational field of Sun with the Lunar Laser Ranging technique, is of
the order of 10^-13. The proposed space-based missions STEP, \muSCOPE, GG and
SEE aim to reach a 10^-15-10^-18 precision level.
