The Space Interferometry Mission (SIM), with its launch date planned f
or 2005, has as its goal astrometry with similar to 1 mu as accuracy f
or stars as faint as 20 mag. If the SIM lives up to expectations, it c
an be used to measure astrometric displacements in the light centroid
caused by gravitational microlensing in the events detected photometri
cally from the ground. The effect is typically similar to 0.1 mas, i.e
., 2 orders of magnitude larger than planned for SLM's accuracy. There
fore, it will be possible to determine the mass, the distance, and the
proper motion of almost any MACHO capable of inducing a photometric m
icrolensing event toward the Galactic bulge or the Magellanic Clouds,
even though no light from the MACHO has to be detected. For strong mic
rolensing events in which the source is photometrically resolved, like
the recent MACHO 95-30 event, SIM's astrometry combined with accurate
ground-based photometry will allow the determination of the angular s
tellar radii, and therefore the effective temperature of the source. T
he effective astrometric cross sections for gravitational lensing by n
earby high proper-motion stars and brown dwarfs are similar to(1 '')(2
), and the effective timescales are similar to 1 yr. SIM will provide
the only practical way to measure masses of single nearby objects with
similar to 1% accuracy. The times of lensing events can be predicted
years in advance.