The Laplace series of ellipsoidal figures of revolution

Результат исследований: Научные публикации в периодических изданияхстатья

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The theory of figures of equilibrium was extensively studied in the nineteenth century, when the reasons for which observed massive celestial bodies (such as the Sun, planets, and satellites) are almost ellipsoidal were discovered. The existence of exactly ellipsoidal figures was established. The gravitational potential of such figures can be represented by a Laplace series whose coefficients (the Stokes constants In) are determined by a certain integral operator. In the case of an ellipsoid of revolution with homothetic equidensites (surfaces of constant density), the general term of this series was found, and for some of the other mass distributions, the first few terms of the series were determined. In this paper, the general term of the series is found in the case where the equidensites are ellipsoids of revolution with oblateness increasing from the center to the surface. Simple estimates and asymptotics of the coefficients In are also found. It turns out that the asymptotics depends only on the mean density, the density on the surface of the outer ellipsoid, and the oblateness of the outer ellipsoid.

Язык оригиналаанглийский
Страницы (с-по)406-413
Число страниц8
ЖурналVestnik St. Petersburg University: Mathematics
Том50
Номер выпуска4
DOI
СостояниеОпубликовано - 1 окт 2017

Отпечаток

Laplace
Figure
Ellipsoid of revolution
Series
Ellipsoid
Term
Coefficient
Stokes
Sun
Integral Operator
Estimate

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  • Математика (все)

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The Laplace series of ellipsoidal figures of revolution. / Kholshevnikov, K. V.; Milanov, D. V.; Shaidulin, V. Sh.

В: Vestnik St. Petersburg University: Mathematics, Том 50, № 4, 01.10.2017, стр. 406-413.

Результат исследований: Научные публикации в периодических изданияхстатья

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