The astrometric and radial velocity techniques of extra-solar planet detection attempt to detect the periodic reflex motion of the parent star by extracting this periodic signal from a time-sampled set of observations. The extraction is generally accomplished using periodogram analysis or the functionally equivalent technique of Least Squares fitting of sinusoids. In this paper, we use a Frequentist approach to examine the sensitivity of Least Squares technique when applied to a combination of radial velocity and astrometric observations. We derive a semi-analytical expression for the sensitivity and show that the combined approach yields significantly better sensitivity than either technique on its own. We discuss the ramifications of this result to upcoming astrometric surveys with FAME, the Keck Interferometer, and SIM.

11 pages, 4 figures (5 EPS files)