Astrometric Microlensing as a Method of Discovering and Characterizing Extra-Solar Planets

We introduce a new method of searching for and characterizing extra-solar 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 lightcurve greatly helps in determining the planetary mass and semi-major axis. 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.