  Atmospheric refraction modifies the apparent position of objects in the sky.
We computed the lateral translation that is to be considered for short-range
applications, such as wavefront sensing and meteor trajectories. We aim to
calculate the lateral shift at each altitude and study its variation according
to meteorological conditions and the location of the observation site. We also
pay special attention to the chromatism of this lateral shift. We extracted the
variation equations of refraction from the geometric tracing of a light ray
path. A numerical method and a dry atmosphere model allowed us to numerically
integrate the system of coupled equations. In addition to this, based on Taylor
expansions, we established three analytic approximations of the lateral shift,
one of which is the one already known in the literature. We compared the three
approximations to the numerical solution. All these estimators are included in
a Python 3.2 package, which is available online. Using the numerical
integration estimator, we calculated the lateral shift values for any zenith
angle including low elevations. The shift is typically around 3 m at a zenith
angle of 45{\deg}, 10 m at 65{\deg}, and even 300 m{\deg} at 85{\deg}. Next,
the study of the variability of the lateral shift as a function of wavelength
shows differences of up to 2% between the visible and near infrared. The
analysis of the errors of each approximation shows the ranges of validity of
the three estimators as a function of the zenith angle. The flat Earth
estimator achieves a relative error of less than 1% up to 55{\deg} while the
new extended second-order estimators improves this result up to 75{\deg}. The
flat Earth estimator is sufficient for applications where the zenith angle is
below 55{\deg} but a refined estimator is necessary to estimate meteor
trajectories at low elevations.
