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  4. On approach to determine the internal potential and gravitational energy of ellipsoid

On approach to determine the internal potential and gravitational energy of ellipsoid

MMC.
2021;
Volume 8, Number 3
: pp. 359–367
https://doi.org/10.23939/mmc2021.03.359
Received: September 04, 2020
Revised: November 17, 2020
Accepted: November 28, 2020

Mathematical Modeling and Computing, Vol. 8, No. 3, pp. 359–367 (2021)

Authors:
  1. Mykhailo Fys
  2. Andrii Brydun
  3. М. I. Yurkiv
1
Department of Cartography and Geospatial Modeling, Institute of Geodesy, Lviv Polytechnic National University
2
Department of Cartography and Geospatial Modeling, Institute of Geodesy, Lviv Polytechnic National University
3
Department of Cartography and Geospatial Modeling, Institute of Geodesy, Lviv Polytechnic National University

Formulas are derived for the calculation of the potential of bodies, which surface is a sphere or an ellipsoid, and the distribution function has a special form: a piecewise continuous one-dimensional function and a three-dimensional mass distribution.  For each of these cases, formulas to calculate both external and internal potentials are derived.  With their help, further the expressions are given for calculation of the potential (gravitational) energy of the masses of such bodies and their corresponding distributions.  For spherical bodies, the exact and approximate relations for determining the energy are provided, which makes it possible to compare the iterative process and the possibility of its application to an ellipsoid.  The described technique has been tested by a specific numerical example.

Internal potential
gravitational energy
Cauchy formula
expansion coefficient
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