Рефракційне подовження траєкторії оптичного сигналу на трансатмосферній трасі

Abstract

Aim. The aim of this work is to improve the accuracy of methods for calculating the tropospheric delay caused by the refractive lengthening of the satellite laser rangefinder signal trajectory on the transatmospheric path. Method. One of the main factors that reduce the accuracy of measuring the distance to artificial Earth satellites with satellite laser rangefinders is the influence of the inhomogeneous Earth troposphere on the rangefinder propagation characteristics. This effect leads to an additional signal delay on the measured path, firstly, due to the differences in its propagation speed in a non-uniform environment from the speed of light in vacuum, and secondly, due to the refractive lengthening of the signal trajectory due to the effect of refraction, which is a result of this inhomogeneity. The refractive lengthening is the difference between the real length of a signal trajectory (with the tropospheric part curved by the refraction) and the distance from the observation point to the satellite in a straight line. The calculations are based on use of the integral form of the geometric optics’ ray equation. With the help of well-known quadrature formulas, this integral form is reduced to a system of algebraic equations connecting the elongation due to refraction and the length of the tropospheric part of the trajectory. The main idea of the new method is the refusal of the widespread use of simplified analytical models of the tropospheric profile when calculating the ratio for the signal trajectory lengthening. In the proposed variant, this ratio is given as an integrated function along the trajectory for values that take into account the actual state of the tropospheric profile at the time of measuring the distance to the satellite. Results. Relationships are obtained for the refractive lengthening and the length of the tropospheric part of the trajectory, which depend on the integral values along the path, namely, the angles of the terrestrial and photogrammetric refraction. Scientific novelty and practical importance. The proposed relations make it possible to determine the refractive elongation through the angles of refraction, which take into account the actual state of the inhomogeneous tropospheric layer for the observed satellite of the Earth immediately at the time of measurements.