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The goal of this paper is to establish the requirements of a barycentriccorrection with an RMS of $\lesssim 1$ cm/s, which is an order of magnitudebetter than necessary for the Doppler detection of true Earth analogs ($\sim9$cm/s). We describe the theory and implementation of accounting for the effectson precise Doppler measurements of motion of the telescope through space,primarily from rotational and orbital motion of the Earth, and the motion ofthe solar system with respect to target star (i.e. the "barycentriccorrection"). We describe the minimal algorithm necessary to accomplish thisand how it differs from a na\"ive subtraction of velocities (i.e. a Galileantransformation). We demonstrate the validity of code we have developed from theCalifornia Planet Survey code via comparison with the pulsar timing package,TEMPO2. We estimate the magnitude of various terms and effects, includingrelativistic effects, and the errors associated with incomplete knowledge oftelescope position, timing, and stellar position and motion. We note thatchromatic aberration will create uncertainties in the time of observation,which will complicate efforts to detect true Earth analogs. Our code isavailable for public use and validation.

Barycentric Corrections at 1 cm/s for precise Doppler velocities