Composition of the fundamental permanent planets of the Earth griup into a single planetary coordinate system
Heading:
| 1Fys, MM, 1Brydun, AM, 1Demkiv, II, 1Khometa, TM 1Lviv Polytechnic National University, Lviv, Ukraine |
| Space Sci. & Technol. 2024, 30 ;(6):84-93 |
| https://doi.org/10.15407/knit2024.06.084 |
| Publication Language: Ukrainian |
Abstract: Two groups of quantities characterize planets as celestial bodies: dynamic compression and parameters of the planet's external gravitational field are specified in different coordinate systems. But modern inquiries of natural sciences about the planets, including the Earth, require the joint application of these parameters, which requires their presentation in a single coordinate system. In most cases, the coefficients of the expansion of the gravitational field to this day are brought to the coordinate system associated with the principal axes of the planetary ellipsoid, in which the dynamic compression is assigned. It is more logical to do the opposite: to express the dynamic compression of the planet in its general planetary rectangular coordinate system, leaving the coefficients of the expansion of the gravitational field in a series unchanged. This significantly reduces the number of calculations and errors when reducing to the planetary coordinate system, which is becoming increasingly used in practice due to its use in GPS technologies.
The paper presents the formula for the dynamic compression of the planet due to all tensors of the second order of the gravitational field of the celestial bodies of the Earth group of the Solar System. The parameters have been reduced to a single rectangular coordinate system for these planets. For specific models of the gravitational field of the planets, we defined the proportionality coefficients with which the inertia tensors are included. Using the example of the planet Earth, the possibility of application in constructing three-dimensional models of the distribution of masses of the interior of the celestial body up to and including the second order is shown, and a comparison of density value calculations in two different coordinate systems is performed. The comparison results confirmed the correctness of the reduction algorithm into one coordinate system.
This approach simplifies the interpretation of the obtained results, as it becomes possible to use the available cartographic materials to visualize the obtained results. This, in turn, makes it possible to connect the peculiarities of the distribution of inhomogeneities of the masses of the planets with the geography of the irregularities of the shape of the celestial body. |
| Keywords: density, dynamic compression, gravitational field, mass distribution, planetary coordinate system |
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