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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.

Язык оригинала | английский |
---|---|

Страницы (с-по) | 318-324 |

Число страниц | 7 |

Журнал | Vestnik St. Petersburg University: Mathematics |

Том | 50 |

Номер выпуска | 3 |

DOI | |

Состояние | Опубликовано - 1 июл 2017 |

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### Предметные области Scopus

- Математика (все)

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**Stokes constants of an oblate ellipsoid of revolution with equidensites homothetic to its surface.** / Kholshevnikov, K. V.; Milanov, D. V.; Shaidulin, V. Sh.

Результат исследований: Научные публикации в периодических изданиях › статья

TY - JOUR

T1 - Stokes constants of an oblate ellipsoid of revolution with equidensites homothetic to its surface

AU - Kholshevnikov, K. V.

AU - Milanov, D. V.

AU - Shaidulin, V. Sh

PY - 2017/7/1

Y1 - 2017/7/1

N2 - 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 In) 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 In have also been obtained.

AB - 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 In) 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 In have also been obtained.

KW - ellipsoid

KW - gravitational potential

KW - Laplace series

UR - http://www.scopus.com/inward/record.url?scp=85029151472&partnerID=8YFLogxK

U2 - 10.3103/S1063454117030098

DO - 10.3103/S1063454117030098

M3 - Article

AN - SCOPUS:85029151472

VL - 50

SP - 318

EP - 324

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -