  We present a vector formulation of an interferometric observation of a star,
including the effects of the barycentric motion of the observatory, the proper
motions of the star, and the reflex motions of the star due to orbiting
planets. We use this model to empirically determine the magnitude and form of
the signal due to a single Earth-mass planet orbiting about a sun-mass star.
Using bounding values for the known components of the model, we perform a
series of expansions, comparing the residuals to this signal. We demonstrate
why commonly used first order linearizations of similar measurement models are
insufficient for signals of the magnitude of the one due to an Earth-mass
planet, and present a consistent expansion which is linear in the unknown
quantities, with residuals multiple orders of magnitude below the Earth-mass
planet signal. We also discuss numerical issues that can arise when simulating
or analyzing these measurements.
