Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978cemec..18..113f&link_type=abstract
Celestial Mechanics, vol. 18, Aug. 1978, p. 113-140.
Astronomy and Astrophysics
Astrophysics
17
Astrophysics, Celestial Mechanics, Spheres, Virial Theorem, Coulomb Potential, Differential Equations, Gravitational Effects, Mass Distribution, Moments Of Inertia, Oscillations, Planetary Evolution, Potential Energy, Relativistic Effects
Scientific paper
A relationship between the potential energy and the moment of inertia of a gravitating spherical body is discovered which appears in the constancy of the product of the form factors for the potential energy and moment of inertia. This relationship is used to obtain an exact solution to Jacobi's virial equation for a gravitating spherical body; the solution represents anharmonic radial oscillations of the body and is valid for a large class of celestial bodies. A relativistic analog of Jacobi's equation is derived for application to such relativistic objects as white dwarfs and neutron stars. Theoretical and experimental data on the frequencies and periods of radial and volumetric oscillations of the sun and planets, including earth, are compared. It is shown that Coulomb forces probably played an important role in the formation of the planets by relating planet mass and average molecular weight.
Denisik S. A.
Ferronskii S. V.
Ferronskii V. I.
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