  Precise radial velocity (PRV) surveys are important for the search of Earth
analogs around nearby bright stars. Such planets induce a small stellar reflex
motion with RV amplitude of $\sim$10 cm/s. Detecting such a small RV signal
poses important challenges to instrumentation, data analysis, and the precision
of astrophysical models to mitigate stellar jitter. In this work, we
investigate an important component in the PRV error budget - the spectral
contamination from the Earth's atmosphere (tellurics). We characterize the
effects of telluric absorption on the RV precision and quantify its
contribution to the RV budget over time and across a wavelength range of 350 nm
- 2.5$\mu$m. We investigate the effectiveness in mitigating tellurics using
simulated spectra of a solar twin star with telluric contamination over a
year's worth of observations, and we extracted the RVs using two commonly
adopted algorithms: dividing out a telluric model before performing
cross-correlation or Forward Modeling the observed spectrum incorporating a
telluric model. We assume various degrees of cleanness in removing the
tellurics, including mimicking the lack of accurate knowledge of the telluric
lines by using a mismatched line profile to model the "observed" tellurics. We
conclude that the RV errors caused by telluric absorption can be suppressed to
close to or even below the photon-limited precision in the optical region,
especially in the blue, around 1-10 cm/s. At red through near-infrared
wavelengths, however, the residuals of tellurics can induce an RV error on the
m/s level even under the most favorable assumptions for telluric removal,
leading to significant systematic noise in the RV time series and periodograms.
If the red-optical or near-infrared becomes critical in the mitigation of
stellar activity, systematic errors from tellurics can be eliminated with a
space mission such as EarthFinder.
