Gravity potential and its component of centrifugal force inside the ellipsoidal planet
Heading:
| 1Fys, MM, 1Zazuliak, PM, 1Sohor, AR 1Lviv Polytechnic National University, Lviv, Ukraine |
| Space Sci. & Technol. 2022, 28 ;(4):71-77 |
| https://doi.org/10.15407/knit2022.04.071 |
| Publication Language: Ukrainian |
Abstract: A method for determining the gravitational potential of a celestial body whose surface is a sphere or ellipsoid with an abrupt mass distribution function is proposed. For these cases, the formulas for determining the internal potential and gravity are obtained. The calculations performed according to these formulas make it possible to analyze the contribution of the ellipticity of the planet to the value of its internal potential and compare it with the magnitude of the centrifugal force for the planets of the Earth group (Earth, Mars, Venus) and the Moon.
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| Keywords: centrifugal force, ellipsoid, gravity, potential, the concept of gravitational disks |
References:
1. Kamensky K. K. (1982). Study of the global features of the level and hypsometric surfaces of Venus. Study of the Earth as a planet by methods of astronomy, geodesy and geophysics: Tr. II Orlov Conf. Kyiv: Naukova Dumka, 80-83.
2. Moritz H. (1994). The Figure of the Earth: Theoretical Geodesy and the Internal Structure of the Earth. Kyiv, 240 p.
3. Fys M. M., Holubinka Y. I., Yurkiv M. I. (2014). Comparative analysis of formulas for the potential and its radial derivatives of three-layer spherical and ellipsoidal planets. Modern achievements of geodetic science and production, I (27), 46--52.
4. Fys M. M., Zayats O. S., Foca R. S., Volos V. O. (2005). On a method for determining the potential of an inhomogeneous ellipsoidal planet. Modern achievements of geodetic science and production, 236-239.
5. Fys M. M., Nikulishyn V. I. (2011). Analysis of the influence of the ellipsoidality of the Earth's figure on its internal structure on the example of the PREM model. Geodynamics, № 1 (10), 17-21.
https://doi.org/10.23939/jgd2011.01.017
6. Fys M. M., Sohor A. R., Nikulishyn V. I. (2013). Potential and its radial derivatives of three-layered spherical planets. Geoinformation Monitoring of the Environment: GNSS and GIS - Technologies: Proc. Int. Sci. and Tech. Symp. Alushta, p. 229-233.
7. Tserklevych A. L., Zayats O. S., Fys M. M. (2012). Gravitational models of three-dimensional distribution of the density of the planets of the terrestrial group. Geodynamics, № 1 (12), 25-34.
https://doi.org/10.23939/jgd2012.01.042
8. Dolifus A. (1972). New optical measurements of planetary diameters. P. 4. Planet Mars. Icarus, 17, № 3, 525-539.
https://doi.org/10.1016/0019-1035(72)90016-4
9. Fys M. M, Brydun A. M.,Yurkiv M. I. (2019). On representation of the internal spherical functions and their derivatives in the planetary coordinate system. Mathematical modeling and computing, 6, № 2, 251-257.
https://doi.org/10.23939/mmc2019.02.251
10. Fys M. M, Brydun A. M., Yurkiv M. I. (2021) On approach to determine the internal potential and gravitational energy of ellipsoid. Mathematical modeling and computing, 8, № 3, 359-367.
https://doi.org/10.23939/mmc2021.03.359
11. Marchenko A. N., Zayats A. S. (2008) Estimation of the potential gravitational energy of the Earth based on reference density models. Geodynamics, № 1 (7), 5-24.