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Section
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Mechanics
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Title
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A non-homogeneous sphere as a model of the planets. Internal points of maximum gravity
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Author(-s)
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Kondratyev B.P.ab,
Trubitsyna N.G.b,
Oparin A.O.b,
Solovyeva P.O.b
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Affiliations
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Pulkovo Observatory of the Russian Academy of Sciencesa,
Udmurt State Universityb
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Abstract
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We obtained the criterion for the existence of gravitational potential inflection points within a inhomogeneous spherical planet. According to the criterion obtained, inflection points (the point of local maximum gravity) can exist only at such a distance $r$ from the center, at which the matter density is two-thirds of the average density of the inner ball with a specified radius. The criterion is defined for the axial moment of the planet inertia too.
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Keywords
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inhomogeneous spheres, Newton's potential, moment of inertia, inflection points of potential, model of the planets
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UDC
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521.1
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MSC
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70F15
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DOI
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10.20537/vm130208
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Received
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1 February 2013
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Language
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Russian
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Citation
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Kondratyev B.P., Trubitsyna N.G., Oparin A.O., Solovyeva P.O. A non-homogeneous sphere as a model of the planets. Internal points of maximum gravity, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 2, pp. 74-84.
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References
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- Duboshin G.N. Teoriya prityazheniya (Theory of gravity), Moscow: Fizmatgiz, 1961, 288 p.
- Snayder P. Dvuhplotnostnaya model Zemnogo shara (Two density model of the Earth), Moscow: Mir, 1988, 160 p.
- Bullen K.E. Plotnost’ Zemli (The density of the Earth), Moscow: Mir, 1978, 245 p.
- Kondratyev B. P. Teoriya potentsiala. Novye metody i zadachi s resheniyami (Potential theory. New methods and problems with solutions), Moscow: Mir, 2007, 512 p.
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Full text
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