Abstract
A relationship between the potential energy and the moment of the inertia for celestial bodies is heuristically discovered. This relationship consists in the constancy of the product of formfactors for the potential energy and the moment of the inertia. The product is independent of the body mass and its radial mass distribution.
We find the exact solution of Jacobi's virial equation for a gravitating spherical body based on the relationship obtained. This solution represents the unharmonic radial oscillations of the body. The solution is valid for a wide class of celestial bodies including variable stars and relativistic objects for which a relativistic analog of Jacob's equation is derived.
The period of the radial oscillations of the planets is estimated with the help of the solution found. We note the coincidence of the experimental data and our theoretical calculations for the Sun.
We show the important role of the Coulomb forces in the formation of the planets. It is demonstrated that the Coulomb forces result in the relation between the planet masses and their average molecular weight.
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Ferronsky, V.I., Denisik, S.A. & Ferronsky, S.V. The solution of Jacobi's virial equation for celestial bodies. Celestial Mechanics 18, 113–140 (1978). https://doi.org/10.1007/BF01228711
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DOI: https://doi.org/10.1007/BF01228711