| 地球引力位球谐级数展开的收敛性研究(英文) |
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| 引用本文： | 申文斌.地球引力位球谐级数展开的收敛性研究(英文)[J].地球空间信息科学学报,2009,12(1):1-6. |
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| 作者姓名： | 申文斌 |
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| 作者单位： | School;Geodesy;Geomatics;Wuhan;University;Laboratory;Geospace;Environment; |
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| 基金项目： | Supported by the National Natural Science Foundation of China (No.40637034, No. 40574004);;the National 863 Program of China (No.2006AA12Z211) |
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| 摘 要： | Given a continuous boundary value on the boundary of a "simply closed surface"S that encloses the whole Earth, a regular harmonic fictitious field V*(P) in the domain outside an inner sphere K i that lies inside the Earth could be determined, and it is proved that V*(P) coincides with the Earth’s real field V(P) in the whole domain outside the Earth. Since in the domain outside the inner sphere Ki and the fictitious regular harmonic function V*(P) could be expressed as a uniformly convergent spherical harm...
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| 关 键 词： | 展开 收敛性 地球引力位 球谐级数 |
Convergence of spherical harmonic series expansion of the Earth’s gravitational potential |
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| Wenbin Shen.Convergence of spherical harmonic series expansion of the Earth’s gravitational potential[J].Geo-Spatial Information Science,2009,12(1):1-6. |
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| Authors: | Wenbin Shen |
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| Institution: | (1) School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan, 430079, China;(2) The Key Laboratory of Geospace Environment and Geodesy, Wuhan University, 129 Luoyu Road, Wuhan, 430079, China |
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| Abstract: | Given a continuous boundary value on the boundary of a “simply closed surface” ∂S that encloses the whole Earth, a regular harmonic fictitious field V*(P) in the domain outside an inner sphere K
i
that lies inside the Earth could be determined, and it is proved that V*(P) coincides with the Earth’s real field V(P) in the whole domain outside the Earth. Since in the domain outside the inner sphere K
i
and the fictitious regular harmonic function V*(P) could be expressed as a uniformly convergent spherical harmonic series, it is concluded that the Earth’s potential field
could be expressed as a uniformly convergent spherical harmonic expansion series in the whole domain outside the Earth.
Supported by the National Natural Science Foundation of China (No.40637034, No. 40574004), the National 863 Program of China
(No. 2006AA12Z211). |
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| Keywords: | potential field fictitious field uniqueness of the solution spherical harmonic series uniform convergence |
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