Refractive lengthening of signal trajectories in satellite laser ranging

A. Prokopov, O. Oliinyk, I. Trevoho
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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.
卫星激光测距中信号轨迹的折射加长
的目标。本文的目的是为了提高卫星激光测距仪信号在跨大气路径上的折射率延长引起的对流层延迟计算方法的精度。方法。卫星激光测距仪测量人造地球卫星距离精度的主要影响因素之一是地球对流层的非均匀性对测距仪传播特性的影响。这种效应导致测量路径上的额外信号延迟,首先是由于其在非均匀环境中的传播速度与真空中的光速不同,其次是由于这种非均匀性导致的折射效应导致信号轨迹的折射延长。折射率延长是指信号轨迹的实际长度(对流层部分被折射率弯曲)与观测点到卫星的直线距离之差。计算是基于几何光学射线方程的积分形式。借助众所周知的正交公式,这种积分形式被简化为一个代数方程组,将由于折射引起的伸长与轨道对流层部分的长度联系起来。新方法的主要思想是在计算信号轨迹延长比时,摈弃了普遍使用的对流层剖面简化解析模型。在提议的变式中,这个比值是作为沿轨迹的积分函数给出的,其值考虑了测量到卫星距离时对流层剖面的实际状态。结果。得到了轨道对流层部分的折射加长与长度的关系,这取决于沿路径的积分值,即地面折射角和摄影测量折射角。科学的新颖性和实用的重要性。该关系式考虑了观测地球卫星在测量时对流层非均匀层的实际状态,从而可以通过折射率角确定折射率延伸。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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