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Russia Izhevsk; Saint Petersburg
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.
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