Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102205
Title: On the representation of the gravitational potential of several model bodies
Authors: Kuznetsov, E. D.
Kholshevnikov, K. V.
Shaidulin, V. S.
Issue Date: 2016
Publisher: Springer New York LLC
Citation: Kuznetsov E. D. On the representation of the gravitational potential of several model bodies / E. D. Kuznetsov, K. V. Kholshevnikov, V. S. Shaidulin. — DOI 10.3103/S1063454116030079 // Vestnik St. Petersburg University: Mathematics. — 2016. — Vol. 49. — Iss. 3. — P. 290-298.
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.
Keywords: GRAVITATIONAL POTENTIAL
LAPLACE SERIES
RATE OF CONVERGENCE
URI: http://hdl.handle.net/10995/102205
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 84990946500
PURE ID: 1232958
7492d058-d7f0-4c7f-8e3c-a6e114950f21
ISSN: 10634541
DOI: 10.3103/S1063454116030079
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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