Global modelling of the gravitational field of irregular bodies using spheroidal approximation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F25%3A43976855" target="_blank" >RIV/49777513:23520/25:43976855 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Global modelling of the gravitational field of irregular bodies using spheroidal approximation

Popis výsledku v původním jazyce

The determination of gravitational fields generated by planetary bodies represents a fundamental task in modern geodesy. To facilitate the computation of gravitational field functionals, we approximate the shapes of individual planetary bodies. The spherical approximation is the most popular, as it conveniently employs numerous symmetries of the sphere. Generally, however, planetary bodies are flattened at the poles or even at the equators. Therefore, a conceptual framework on the spheroidal approximation should be analysed. In this contribution, we develop a new mathematical theory for modelling gravitational fields generated by irregular bodies. Specifically, the gravitational potential, the components of the gravitational gradient, and the second- and third-order gravitational tensor components are parametrised using spheroidal harmonic functions defined within the minimal Brillouin spheroid. To enable global calculation, especially near the poles, the original spheroidal harmonic expansions are transformed into their non-singular counterparts. Additionally, we investigate selected numerical aspects of the Legendre functions of the first and second kind. Numerical experiments are performed to validate the proposed approach. Both singular and non-singular formulations are systematically evaluated.

Název v anglickém jazyce

Global modelling of the gravitational field of irregular bodies using spheroidal approximation

Popis výsledku anglicky

The determination of gravitational fields generated by planetary bodies represents a fundamental task in modern geodesy. To facilitate the computation of gravitational field functionals, we approximate the shapes of individual planetary bodies. The spherical approximation is the most popular, as it conveniently employs numerous symmetries of the sphere. Generally, however, planetary bodies are flattened at the poles or even at the equators. Therefore, a conceptual framework on the spheroidal approximation should be analysed. In this contribution, we develop a new mathematical theory for modelling gravitational fields generated by irregular bodies. Specifically, the gravitational potential, the components of the gravitational gradient, and the second- and third-order gravitational tensor components are parametrised using spheroidal harmonic functions defined within the minimal Brillouin spheroid. To enable global calculation, especially near the poles, the original spheroidal harmonic expansions are transformed into their non-singular counterparts. Additionally, we investigate selected numerical aspects of the Legendre functions of the first and second kind. Numerical experiments are performed to validate the proposed approach. Both singular and non-singular formulations are systematically evaluated.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10508 - Physical geography

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů