Study of the lateral shift due to atmospheric refraction: alternative analytical methods, and new results

Atmospheric refraction modifies the apparent position of objects in the sky, and also produces a progressive lateral shift of the light rays received from these objects; in the case of a spherically symmetric atmosphere, for the first time, this shift has been numerically studied in 2022, and different analytical estimators have been compared (by Labriji et al.) for the total shift. This topic is important for the reconstruction of meteor trajectories, for the analysis of wavefront sensing in adaptative optics, etc. Always in the case of a spherically symmetric atmosphere, we show two other analytical methods to study this lateral shift, and to be able to estimate it analytically in the difficult case when the celestial object is seen near the astronomical horizon. One of these methods allows us to deduce an estimator, not only of the total shift, but also of the shift of any point of the ray. We compare properties of the total lateral shift and of the refraction angle, and also the chromatism of the total lateral shift to the chromatism of the air refractivity, for rays coming from an object seen either high enough above the astronomical horizon, or on it. In this latter case, our first method shows departures from proportionality between the chromatisms of the air refractivity, of the astronomical refraction angle, and, even more, of the total lateral shift.