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The goal of this paper is to establish the requirements of a barycentric correction with an RMS of $lesssim 1$ cm/s, which is an order of magnitude better than necessary for the Doppler detection of true Earth analogs ($sim9$ cm/s). We describe the theory and implementation of accounting for the effects on precise Doppler measurements of motion of the telescope through space, primarily from rotational and orbital motion of the Earth, and the motion of the solar system with respect to target star (i.e. the barycentric correction). We describe the minimal algorithm necessary to accomplish this and how it differs from a naive subtraction of velocities (i.e. a Galilean transformation). We demonstrate the validity of code we have developed from the California Planet Survey code via comparison with the pulsar timing package, TEMPO2. We estimate the magnitude of various terms and effects, including relativistic effects, and the errors associated with incomplete knowledge of telescope position, timing, and stellar position and motion. We note that chromatic aberration will create uncertainties in the time of observation, which will complicate efforts to detect true Earth analogs. Our code is available for public use and validation.
High fidelity iodine spectra provide the wavelength and instrument calibration needed to extract precise radial velocities (RVs) from stellar spectral observations taken through iodine cells. Such iodine spectra are usually taken by a Fourier Transfo
SPIRou is a near-infrared (nIR) spectropolarimeter at the CFHT, covering the YJHK nIR spectral bands ($980-2350,mathrm{nm}$). We describe the development and current status of the SPIRou wavelength calibration in order to obtain precise radial veloci
We present a multi-calibrator solution, i.e. MultiView, to achieve accurate astrometry on the level of the thermal noise at low VLBI frequencies dominated by ionospheric residuals. We demonstrate on L-band VLBA observations how MultiView provides sup
The CHIRON optical high-resolution echelle spectrometer was commissioned at the 1.5m telescope at CTIO in 2011. The instrument was designed for high throughput and stability, with the goal of monitoring radial velocities of bright stars with high pre
We are developing a stable and precise spectrograph for the Large Binocular Telescope (LBT) named iLocater. The instrument comprises three principal components: a cross-dispersed echelle spectrograph that operates in the YJ-bands (0.97-1.30 microns),