Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 46497 10.2205/2019ES000651 ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ Kaula's rule - a consequence of probability laws by A. N. Kolmogorov and his school Kaula's rule - a consequence of probability laws by A. N. Kolmogorov and his school Gledzer E B Gledzer E B Golitsyn G S Golitsyn G S A. M. Obukhov Institute of Atmospheric Physics RAS ru A. M. Obukhov Institute of Atmospheric Physics RAS ru A. M. Obukhov Institute of Atmospheric Physics RAS ru A. M. Obukhov Institute of Atmospheric Physics RAS ru 19 6 29 10 2021 https://rjes.ru/en/nauka/article/46497/view

The paper analyzes a possible cause for the universal behavior of the covariating fluctuations of planet gravity. The consideration based on the idea that the topography fluctuations are governed by a random Markov process leads to universal dependence k−2" role="presentation" style="position: relative;">k-2k-2k^{-2} with k" role="presentation" style="position: relative;">kkk being the amplitudes of the j" role="presentation" style="position: relative;">jjj-th spherical harmonic of the terrain profile. This law known as the Kaula's rule is then derived from the solution of the Fokker - Plank equation for the fluctuations of the terrain profile as the function of the horizontal coordinate. The respective diffusivities for Earth and Venus are retrieved from the existing data.

The paper analyzes a possible cause for the universal behavior of the covariating fluctuations of planet gravity. The consideration based on the idea that the topography fluctuations are governed by a random Markov process leads to universal dependence k−2" role="presentation" style="position: relative;">k-2k-2k^{-2} with k" role="presentation" style="position: relative;">kkk being the amplitudes of the j" role="presentation" style="position: relative;">jjj-th spherical harmonic of the terrain profile. This law known as the Kaula's rule is then derived from the solution of the Fokker - Plank equation for the fluctuations of the terrain profile as the function of the horizontal coordinate. The respective diffusivities for Earth and Venus are retrieved from the existing data.

 Kaula's rule Thumb rule planet gravity Fokker-Planck equation Kaula's rule Thumb rule planet gravity Fokker-Planck equation We thank A. A. Lushnikov for carefully reading the manuscript and indicating some errors in the formulas. This work has been particularly supported by the RAS Presidium Program No. 7 "The development of non-linear methods in theoretical and mathematical physics". The authors are very thankful to Dr. O. G. Chkhetiany for discussion of the results and his continuous help during the long work.

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