Stokes constants of an oblate ellipsoid of revolution with equidensites homothetic to its surface
| Autor: | V. Sh. Shaidulin, D. V. Milanov, Konstantin V. Kholshevnikov |
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| Rok vydání: | 2017 |
| Předmět: |
Surface (mathematics)
Mass distribution Series (mathematics) Laplace transform General Mathematics 010102 general mathematics Mathematical analysis 01 natural sciences Ellipsoid Flattening Homothetic transformation Gravitational potential Classical mechanics 0103 physical sciences 0101 mathematics 010303 astronomy & astrophysics Mathematics |
| Zdroj: | Vestnik St. Petersburg University, Mathematics. 50:318-324 |
| ISSN: | 1934-7855 1063-4541 |
| Popis: | The theory of equilibrium figures was actively developed in the 19th century, when it was found that the observed massive celestial bodies (the Sun, planets, and satellites) had an almost ellipsoidal form. The existence of exactly ellipsoidal figures was also established. The gravitational potential of these figures is represented by a Laplace series with its coefficients (Stokes’ constants I n ) determined by some integral operator. The general term of the series was found for a homogeneous ellipsoid of revolution and the first terms of the series were found for some other mass distributions. Here, we have obtained the general term of the series for an arbitrary mass distribution given that the equidensites (surfaces of equal density) are homothetic to the outer surface of the ellipsoid of revolution. Simple estimates and an asymptotics of I n have also been obtained. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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