Vestnik КRAUNC. Fiz.-Mat. nauki. 2023. vol. 44. no. 3. P. 130-143. ISSN 2079-6641


Research Article

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To the Question of an Qnalytical Estimate Some Internal Sizes of the Earth

S. O. Gladkov^\ast

Moscow Aviation Institute, 125993, Moscow, Volokolamskoe sh., 4, Russia

Abstract. Using a model representation of the motion of the Earth’s core in a viscous continuum its equation of motion is obtained and the linear size of the barispheric is analytically found. A completely adequate estimate of the distance from the center of the Earth to the center of mass of the core is given which does not contradict modern geodetic ideas. It is shown that the proposed model, which is not related to the measurement of the velocities of longitudinal and transverse seismic waves, makes it possible to determine quite satisfactorily all the basic geometric parameters of the barisphere. In addition, the main advantage of this approach is also associated with the possibility of analytically solving the resulting equations, which gives us a completely justified and objective model that allows us to predict a number of geometric parameters relating to the internal structure of the Earth and making it possible to evaluate them numerically. The described approach can be applied to solving individual geophysical problems, one of which can be considered, for example, the molten outer core in the form of a non-Newtonian fluid, the dynamic viscosity of which increases with increasing distance from the center of the Earth.

Key words: equations of motion, density of the Earth, lithosphere, core of the Earth, barisphere.

Received: 24.08.2023; Revised: 19.09.2023; Accepted: 01.11.2023; First online: 02.11.2023

For citation. Gladkov S. O. To the question of an analytical estimate some internal sizes of the Earth. Vestnik KRAUNC. Fiz.-mat. nauki. 2023, 44: 3, 130-143. EDN: BGYLAW.

Funding. The study was carried out without support from foundations

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. The author participated in the writing of the article and is fully responsible for
submitting the final version of the article to the press.

^\astCorrespondence: E-mail:

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Gladkov S. O., 2023

© Institute of Cosmophysical Research and Radio Wave Propagation, 2023 (original layout, design, compilation)


  1. Furth R. On the equation of state of solids. Proc. Roy. Soc. 1944. vol. 183. pp. 223 – 234.
  2. Kozlovskaya S. V. Sravnitel’nyy analiz vnutrennego stroyeniya i sostava zemnykh planet i sputnikov. DAN SSSR. 1953. vol. 92. no. pp. 903-906.(In Russian).
  3. Levin B. Yu. Sostav Zemli. Trudy Geofizicheskogo instituta [Composition of the Earth]. 1955. vol. 26. AN SSSR.(In Russian).
  4. Zharkov V. N. Fizika yadra Zemli [Physics of the Earth’s core]. Trudy instituta fiziki Zemli. 1962. vol. 20.(In Russian).
  5. Magnitskiy V. A. Osnovy fiziki Zemli [Fundamentals of Earth physics]. Mosow. Geodezizdat, 1963.(In Russian).
  6. Stishov S. M. O vnutrennem stroyenii Zemli. Geokhimiya.1962. no. 8.(In Russian).
  7. Zharkov V. N. Vnutrenneye stroyeniye Zemli i Planet [Internal structure of the Earth and Planets]. Moscow. Nauka, 1978. 191 p.(In Russian).
  8. Kiselev V. M. Neravnomernost’ sutochnogo vrashcheniya Zemli [Irregularity of the Earth’s daily rotation]. Novosibirsk. Nauka, 1980. 160 p.(In Russian).
  9. Magnitskiy V. A. Obshchaya geofizika [General geophysics]. Moscow. Izdatel’stvo MGU, 1995. 318 p.
  10. Ovtchinnikov V. M., Krasnoshchekov D. N. Izvestiya, Physics of the Solid Earth. 2021. vol. 57. no. 2. pp. 141-162. DOI:10.1134/S1069351321020087
  11. Magnitskiy V. A. Vnutrenneye stroyeniye i fizika Zemli [Internal structure and physics of the Earth]. Мoscow. Nedra. 1965. 379 p.(In Russian).
  12. Steysi F. Fizika Zemli [Physics of the Earth]. Мoscow. Mir, 1972. 342 p.(In Russian).
  13. Sivukhin D. V. Obshchiy kurs fiziki. Mekhanika [General physics course. Mechanics]. vol. 1. Мoscow. Fizmatlit, 2010. 560 p.(In Russian).
  14. Smirnov V. I. Kurs vysshey matematiki [Course of higher mathematics]. vol. 1. Мoscow. Nauka, 1967. 479 p.(In Russian).
  15. Gladkov S. O. On Calculating the Stopping Time of a Cylindrical Body Rotating in a Viscous Continuum and the Time of Entrainment of a Coaxial External Cylinder. Technical Physics. 2018. vol. 63. no. 3. pp. 325-330. DOI:10.1134/S1063784218030088.

Information about author

Gladkov Sergey Oktyabrinovich – D.Sc. (Phys. & Math.), Professor, Associate Professor of the Department of Applied Software and Mathematical Methods, Moscow Aviation Institute (National Research University), Moscow, Russia,
ORCID 0000-0002-2755-9133.