### 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} ^{+} ^{1}Y_{n}(θ, λ) with R being the radius of the enveloping T sphere. The surface harmonic Y_{n} 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 language | English |
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Pages (from-to) | 75-94 |

Number of pages | 20 |

Journal | Celestial Mechanics and Dynamical Astronomy |

Volume | 128 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 May 2017 |

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### Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

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

Research output

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 -