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Till now, we can obtain information about the internal structure of the planets only on the basis of Space Research of the gravity field and the topography of the planets. It is known that the inverse problem of gravimetry is incorrect, and its solution is possible only in attracting additional information about the internal structure, and based on some theoretical conclusions. These conclusions are based on cosmogonic scenarios for the formation of terrestrial planets, on geophysical and geochemical information and data on high-energy physics. Unfortunately, such data are currently available only for the Earth, which, based on the interpretation of seismological and seismic observations and analysis of the splitting of the normal modes of the free oscillations of the Earth have been identified depth ranges of maximum anomalies of lateral variations of density and seismic wave velocities. We have developed a method of determining the anomalous internal structure terrestrial planets only on the basis of Space Research [1, 2]. The essence of this method is the determination of the possible depths of compensation for expansion harmonics of topographic heights relative to the equilibrium ellipsoid for different-order and different-degree harmonics. Since each topographic irregularity is characterized by a certain set of the harmonics, the maximal concentration of compensation of this set within a certain limited depth interval can point to the most probable depths of compensation of the considered topographic irregularity. If we find the depths of compensation in such a way, we will be able to solve the formulated problem, i.e. to find the lateral distribution of the anomalous masses at different depths for the terrestrial planets. We applied our method to study the internal structure of the Earth, comparing the obtained results with the seismological and free-oscillation data, and to the study of Mars, for which there are no such observations. Comparative analysis of the results is given in [3]. Reference 1. Chuikova N.A., Nasonova L.P. , and Maksimova T.G. Anomalous structure of the Crust and Mantle of Mars. ISSN 0027-1349, Moscow University Physics Bulletin, 2011, Vol.66, No. 1, pp. 64-71 2. Chuikova N.A., Nasonova L.P. , and Maksimova T.G. Anomalies of Density, Stresses, and the Gravitational Field in the Interior of Mars. ISSN 0027-1349, Moscow University Physics Bulletin, 2012, Vol.67, No. 2, pp. 218-225 3. Chuikova N.A., Nasonova L.P. , and Maksimova T.G Density, Stress, and Gravity Anomalies in the Interiors of the Earth and Mars and the Probable Geodynamical Implications: Comparative Analysis. ISSN 1069_3513, Izvestiya, Physics of the Solid Earth, 2014, Vol. 50, No. 3, pp. 427–443.