We have investigated an expected deviation of the positions or the proper motions of stars as the cosmic error caused by the gravitational microlensing effect. In observing stars in the Galactic bulge region, we obtain an expected deviation of a star positions by the gravitational microlensing effect of about 7 μas. We have also estimated the expected deviation of the proper motions of stars in the Galactic bulge caused by the gravitational microlensing effect. The expected deviation of the proper motions is mainly caused by the lens object located at the nearest angular distance from the source star. Each deviation of the proper motion has a value of less than 0.02 μas yr–1 for 99% of the sources. We have investigated the correlation of the deviation of Galactic bulge stars caused by the gravitational microlensing effect. The value of the correlation angle of the positional deviation is estimated to be about 1 arcmin. In the same way, we have estimated the correlation angle of the deviation of the proper motions. The angle is estimated to be about 1 arcsec. The following difference distinguishes the deviation of the position and that of the proper motion. The positional deviation is affected not only by lenses near the source but also by the lenses far from the source. On the other hand, the deviation of the proper motion by microlensing is mainly only caused by the nearest lens from the source. This difference causes that of the correlation angle.
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