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

Research output

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’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.

Original languageEnglish
Pages (from-to)75-94
Number of pages20
JournalCelestial Mechanics and Dynamical Astronomy
Volume128
Issue number1
DOIs
Publication statusPublished - 1 May 2017

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Exactness
Laplace
Irregular
Modulus Function
Series
Spherical Harmonics
spherical harmonics
Brackets
Term
estimates
Unit Sphere
Estimate
Harmonic
Radius
celestial bodies
mountain
brackets
mountains
gravitational fields
harmonics

Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

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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’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.",
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AU - Shaidulin, Vakhit Sh

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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.

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