On the exactness of estimates for irregularly structured bodies of the general term of Laplace series

Standard

On the exactness of estimates for irregularly structured bodies of the general term of Laplace series. / Kholshevnikov, Konstantin V.; Shaidulin, Vakhit Sh.

в: Celestial Mechanics and Dynamical Astronomy, Том 128, № 1, 01.05.2017, стр. 75-94.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{e14d4fe6b6ed49ff859603c0b0aafc3d,

title = "On the exactness of estimates for irregularly structured bodies of the general term of Laplace series",

abstract = "The main form of the representation of a gravitational potential V for a celestial body T in outer space is the Laplace series in solid spherical harmonics (R/ r) n + 1Yn(θ, λ) with R being the radius of the enveloping T sphere. The surface harmonic Yn satisfies the inequality(Formula presented.)The angular brackets mark the maximum of a function{\textquoteright}s modulus over a unit sphere. For bodies with an irregular structure σ= 5 / 2 , and this value cannot be increased generally. However, a class of irregular bodies (smooth bodies with peaked mountains) has been found recently in which σ= 3. In this paper, we will prove the exactness of this estimate, showing that a body belonging to the above class does exist and (Formula presented.)for it.",

keywords = "Exact estimate of a general term of a series, Gravitational potential, Irregular bodies, Laplace series",

author = "Kholshevnikov, {Konstantin V.} and Shaidulin, {Vakhit Sh}",

year = "2017",

month = may,

day = "1",

doi = "10.1007/s10569-016-9742-8",

language = "English",

volume = "128",

pages = "75--94",

journal = "Celestial Mechanics and Dynamical Astronomy",

issn = "0923-2958",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - On the exactness of estimates for irregularly structured bodies of the general term of Laplace series

AU - Kholshevnikov, Konstantin V.

AU - Shaidulin, Vakhit Sh

PY - 2017/5/1

Y1 - 2017/5/1

N2 - The main form of the representation of a gravitational potential V for a celestial body T in outer space is the Laplace series in solid spherical harmonics (R/ r) n + 1Yn(θ, λ) with R being the radius of the enveloping T sphere. The surface harmonic Yn satisfies the inequality(Formula presented.)The angular brackets mark the maximum of a function’s modulus over a unit sphere. For bodies with an irregular structure σ= 5 / 2 , and this value cannot be increased generally. However, a class of irregular bodies (smooth bodies with peaked mountains) has been found recently in which σ= 3. In this paper, we will prove the exactness of this estimate, showing that a body belonging to the above class does exist and (Formula presented.)for it.

AB - The main form of the representation of a gravitational potential V for a celestial body T in outer space is the Laplace series in solid spherical harmonics (R/ r) n + 1Yn(θ, λ) with R being the radius of the enveloping T sphere. The surface harmonic Yn satisfies the inequality(Formula presented.)The angular brackets mark the maximum of a function’s modulus over a unit sphere. For bodies with an irregular structure σ= 5 / 2 , and this value cannot be increased generally. However, a class of irregular bodies (smooth bodies with peaked mountains) has been found recently in which σ= 3. In this paper, we will prove the exactness of this estimate, showing that a body belonging to the above class does exist and (Formula presented.)for it.

KW - Exact estimate of a general term of a series

KW - Gravitational potential

KW - Irregular bodies

KW - Laplace series

UR - http://www.scopus.com/inward/record.url?scp=84995784210&partnerID=8YFLogxK

U2 - 10.1007/s10569-016-9742-8

DO - 10.1007/s10569-016-9742-8

M3 - Article

AN - SCOPUS:84995784210

VL - 128

SP - 75

EP - 94

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 1

ER -

ID: 15489528