  Current precision in radial velocity (RV) measurements of binary stars
reaches $\sim$2 ms$^{-1}$. This level of precision means that RV models have to
take into account additional non-Keplerian effects such as tidal and rotational
distortion of the components of a binary star, relativistic effects and orbital
precession.
  We generate synthetic binaries using Yonsei-Yale stellar models. For typical
representatives we investigate the impact of various orbital orientations and
different non-Keplerian effects on the RV curves. To this end we simulate RV
observations with an added white noise of different scale. Subsequently we try
to reconstruct the input orbital parameters and their errors by fitting a model
using a standard least-squares method. In particular we investigate the
connection between the tidal distortion of the shape of the stars and the
best-fit orbital eccentricity, the possibility of deriving orbital inclination
of a non-eclipsing binary star by exploiting relativistic effects and the
circumstances in which the orbital precession can be detected.
  We confirm that the method proposed by to obtain orbital inclination with use
of the relativistic effect does work in favourable cases and that it can be
used even for orbital configurations far from an edge-on orientation. We show
that the RV variations imposed by tidally distorted stars can mimic non-zero
eccentricity in some binaries. The scale of such an effect depends on the RV
accuracy. Finally, we demonstrate that the apsidal precession can be easily
detected with precision RVs. In particular we can detect orbital precession of
$10^{-4}$ rad yr$^{-1}$, $10^{-3}$ rad yr$^{-1}$ for precision of RVs of 1
ms$^{-1}$ and 10 ms$^{-1}$ respectively.
