The use of the synthetic method of harmonic analysis for investigating the structure of space natural bodies

This chapter considers a method for investigating the topographic model of theMoon’s surface based on harmonicmulti-parameter analysis and fractal geometry. The data from the “Clementine”, “Kaguya” and “LRO” satellite space missions were used as observational material. The Russian plans include carrying out works that will provide referencing of the lunar surface images to the selenographic coordinate system. The implementation of those plans may bring selenodesy to a level comparable to the Earth’s geodesy. At the same time, data analysis in the projects mentioned above put increased demands on the description of the complex dynamic and gravity model of the Moon’s structure. The observations produced at space missions refer to the so-called quasi-dynamic system whose origin coincides with the lunar center of mass, but axes have a shift concerning the lunar axes of inertia. Many lunar maps have a quasi-dynamic system. The main purposes of this work are related to the construction of theoretical models of the physical surface based on modern satellite measurements. An analysis of fractal dimensions and self-similarity coefficients of both individual local zones and the global model of the entire lunar sphere was conducted. As a result, similar zones of the lunar surface formed at the same physical processes were determined. These results are significant for constructing a theory of the Moon’s evolution