On the representation of the gravitational potential of several model bodies / Kuznetsov E.D., Kholshevnikov K.V., Shaidulin V.S. // Vestnik St. Petersburg University: Mathematics. - 2016. - V. 49, l. 3. - P. 290-298.

ISSN:

10634541

Type:

Article

Abstract:

A Laplace series of spherical harmonics Yn(θ, λ) is the most common representation of the gravitational potential for a compact body T in outer space in spherical coordinates r, θ, λ. The Chebyshev norm estimate (the maximum modulus of the function on the sphere) is known for bodies of an irregular structure:〈Yn〉 ≤ Cn–5/2, C = const, n ≥ 1. In this paper, an explicit expression of Yn(θ, λ) for several model bodies is obtained. In all cases (except for one), the estimate 〈Yn〉 holds under the exact exponent 5/2. In one case, where the body T touches the sphere that envelops it,〈Yn〉 decreases much faster, viz.,〈Yn〉 ≤ Cn–5/2pn, C = const, n ≥ 1. The quantity p < 1 equals the distance from the origin of coordinates to the edge of the surface T expressed in enveloping sphere radii. In the general case, the exactness of the exponent 5/2 is confirmed by examples of bodies that more or less resemble real celestial bodies [16, Fig. 6]. © 2016, Allerton Press, Inc.

Author keywords:

gravitational potential; Laplace series; rate of convergence

Index keywords:

нет данных

DOI:

10.3103/S1063454116030079

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https://www.scopus.com/inward/record.uri?eid=2-s2.0-84990946500&doi=10.3103%2fS1063454116030079&partnerID=40&md5=56573cf0f4afe020b1b73bc2d8155031

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Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-84990946500&doi=10.3103%2fS1063454116030079&partnerID=40&md5=56573cf0f4afe020b1b73bc2d8155031
Affiliations	Ural Federal University, ul. Mira 19, Ekaterinburg, Russian Federation; St. Petersburg State University, Universitetskaya nab. 7–9, St. Petersburg, Russian Federation; Institute of Applied Astronomy, Russian Academy of Sciences, nab. Kutuzova 10, St. Petersburg, Russian Federation; Main (Pulkovo) Astronomical Observatory, Russian Academy of Sciences, Pulkovskoe sh. 65/1, St. Petersburg, Russian Federation
Author Keywords	gravitational potential; Laplace series; rate of convergence
References	Duboshin, G.N., (1961) Theory of Attraction, , Fizmatlit, Moscow; Kaula, W., (1970) Theory of satellite geodesy, , Blaisdell, Waltham, MA; Burša, M., (1970) Fundamentals of Space Geodesy, Vol. 2: Dynamic Cosmic Geodesy, , Minist. Nár. Obrany, Prague; Grushinskii, N.P., (1976) Theory of the Earth Figure, , Nauka, Moscow; Kondrat’ev, B.P., (2003) Theory of Potential and Figures of Equilibrium, , Inst. Komp. Issled., Moscow; Vatrt, V., Truncation error due to geopotential model EGM96 (1999) Stud. Geophys. Geod., 43, pp. 223-227; Pavlis, N.K., Holmes, S.A., Kenyon, S.C., Factor, J.K., An Earth gravitational model to degree 2160: EGM2008 (2008) General Assembly of the European Geosciences Union, Vienna, Apr. 13–18; Petrovskaya, M.S., Vershkov, A.N., The construction of gravitational field models on the basis of satellite measurements of gravitational potential derivatives (2014) Cosmic Res., 52, pp. 166-174; Natanson, I.P., Constructive Function Theory (1964) Uniform approximation, , GITTL, Moscow; Hobson, E.W., (1931) The Theory of Spherical and Ellipsoidal Harmonics, , Cambridge Univ. Press, Cambridge; Szegö, G., Orthogonal Polynomials (1959) Ser. AMS Colloquium Publications, , Am. Math. Soc., New York; Antonov, V.A., Timoshkova, E.I., Kholshevnikov, K.V., (1988) Introduction to the Theory of Newtonian Potential, , Nauka, Moscow; Yarov-Yarovoi, M.S., On the force-function of the attraction of a planet and its satellite (1963) Problems of Motion of Artificial Celestial Bodies, , Akad. Nauk SSSR, Moscow; Kholshevnikov, K.V., Shaidulin, V.S., On the gravitational potential of a spherical segment (2015) Vestn. St. Petersburg Univ.: Math., 48, pp. 49-54; Antonov, V.A., Kholshevnikov, K.V., Shaidulin, V.S., Estimating the derivative of the Legendre polynomial (2010) Vestn. St. Petersburg Univ.: Math., 43, pp. 191-197; Kholshevnikov, K.V., Shaidulin, V.S., On properties of integrals of the Legendre polynomial (2014) Vestn. St. Petersburg Univ.: Math., 47, pp. 28-38
Correspondence Address	Kuznetsov, E.D.; Ural Federal University, ul. Mira 19, Russian Federation; email: eduard.kuznetsov@urfu.ru
Publisher	Springer New York LLC
Language of Original Document	English
Abbreviated Source Title	Vestnik St. Petersburg Univ. Math.
Source	Scopus