Astrometric microlensing as a method of discovering and characterizing extrasolar planets

We introduce a new method of searching for and characterizing extrasolar planets. We show that by monitoring the center-of-light motion of microlensing alerts using the next generation of high-precision astrometric instruments the probability of detecting a planet orbiting the lens is high. We show that adding astrometric information to the photometric microlensing light curve greatly helps in determining the planetary mass and projected separation. We introduce astrometric maps as a new way for calculating astrometric motion and planet detection probabilities. Finite source effects are important for low-mass planets, but even Earth-mass planets can give detectable signals.