ON THE NATURE OF THE RADIAL AND CROSS TRACK ERRORS FOR ARTIFICIAL EARTH SATELLITES

摘要

In this paper we discuss the analysis of the radial and cross track errors of artificial Earth satellites in terms of the interference of two one dimensional celestial mechanical wave trains. The resulting equations for these tracking errors describe the behavior of the uncertainties in the orbital parameters as oscillatory in nature, with a rapidly oscillating term, which is a function of the sum of the observed and computed orbital frequencies, modulated in amplitude by a slowly varying oscillation. This latter term is itself a function of either the difference between these orbital frequencies or between the values of the computed and observed right ascensions, depending upon whether it is the radial or cross track case under consideration. In theoretical physics, this effect is referred to as the phenomenon of beats and is common in the physics of sound and elastic media.