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## Archive of Issues

Russia Izhevsk; Saint Petersburg
Year
2013
Issue
2
Pages
74-84
 Section Mechanics Title A non-homogeneous sphere as a model of the planets. Internal points of maximum gravity Author(-s) Kondratyev B.P.ab, Trubitsyna N.G.b, Oparin A.O.b, Solovyeva P.O.b Affiliations Pulkovo Observatory of the Russian Academy of Sciencesa, Udmurt State Universityb Abstract 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. Keywords inhomogeneous spheres, Newton's potential, moment of inertia, inflection points of potential, model of the planets UDC 521.1 MSC 70F15 DOI 10.20537/vm130208 Received 1 February 2013 Language Russian Citation 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. References 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. Full text