Sensitivity of the astrometric technique in detecting outer planets

With the advent of optical interferometers that will be coming on line in t he next decade, radial velocity searches for extrasolar planets will be com plemented by high angular resolution astrometric measurements. In this pape r, we explore the sensitivity of the astrometric technique, and develop an analytical understanding of the sensitivity in the regime where the orbital period is longer than the time baseline of the survey. As in an earlier pa per that dealt with the radial velocity technique, our analysis of the astr ometric technique utilizes both the orbital amplitude and phase.