Perturbative approach to astrometric microlensing due to an extrasolar planet

We have developed a perturbative approach to microlensing due to an extrasolar planetary lens. In particular, we have found analytic formulae for triple images. We use the formulae to investigate the astrometric microlensing due to the extrasolar planetary lens, in expectation of dramatic improvements in the precision of the future astrometric measurements. For a weak-lensing case, we show how the maximum angular size and the typical timescale of the anomalous shift of the light centroid are dependent on the mass ratio and angular separation between the star and the planet.