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Features of the Relief Spectrum of the Moon and Planets

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Abstract

The relief spectra of the Moon, Mars and Earth with a very high resolution are discussed (Rexer and Hirt, 2015). According to the Kaula rule (Kaula, 1966), these spectra decay as \({{k}^{{ - 2}}}\). This fact has been recently explained (Gledzer and Golitsyn, 2019) based on the probabilistic laws by Kolmogorov and his school (Kolmogorov, 1934; Obukhov, 1959; Monin and Yaglom, 1967; Golitsyn, 2018; Gledzer and Golitsyn, 2010; Yaglom, 1955). However, the authors (Gledzer and Golitsyn, 2019) have not given a detailed explanation why, for the smallest scales, the relief spectrum of the Moon becomes steeper and behaves like \({{k}^{{ - 4}}}\). The same can be said for Mars and Earth on even smaller spatial scales (Rexer and Hirt, 2015). The explanation has been given by replacing the Markovian character of the probability distribution of accelerations by an internal exponential correlation. Similarity and dimensionality considerations involving the physical properties of the crust make it possible to estimate the scale of the features of the spectra observed.

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ACKNOWLEDGMENTS

The author is grateful to the referee, whose comments led to significant improvements in the article.

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Correspondence to G. S. Golitsyn.

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Translated by G. Dedkov

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Golitsyn, G.S. Features of the Relief Spectrum of the Moon and Planets. Sol Syst Res 55, 31–34 (2021). https://doi.org/10.1134/S0038094621010032

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