The inverse problem of radiotransillumination of the earth's troposphere along a path between the earth and the satellite is solved theoretically, based on Tikhonov's method of regularization for a one-dimensional spherically layered model, and experimentally. Numerical modeling is performed for conditions of normal and anomalous propagation of radio waves. The algorithm was used to determine the different altitude profiles of the refractive index of the troposphere from measurements of the Doppler shift of the frequency of radio signals from a satellite.