Physical Meaning of Dynamical Equilibrium of a Celestial Body

  • V. I. Ferronsky
  • S. V. Ferronsky


Interpretation of the artificial satellite data proving the absence of the hydrostatic equilibrium state of the Earth and the Moon are discussed in detail. It is shown that the Earth and the Moon are triaxial bodies, and their axial rotation is not an inertial effect. Observational data from earthquakes demonstrate the planet’s oscillating dynamics with periods from 8.4 to 57 min. Two general modes of the Earth’s oscillation were found, namely, spectral with a vector of radial direction and torsion with a vector perpendicular to the radius.

The main problem of a celestial body’s equilibrium state, which is a ratio of the kinetic and potential energies, is discussed thoroughly. It is shown that the ratio of Earth’s kinetic and potential energy is equal to ∼1/300. The other planets, the Sun, and the Moon, the hydrostatic equilibrium for which is also accepted as a fundamental condition, stay in analogous situation. This is because the hydrostatic approach does not take into account the kinetic energy of the interacted elementary mass particles, which is, in fact, Newton’s energy of gravity (and force). As a result, celestial body dynamics have been left without kinetic energy.

In order to correct this situation, the generalized virial theorem was derived by introduction of the volumetric forces and moments into the classic one. As a result, the oscillating mode of the body motion has appeared in the form of Jacobi’s virial equation in the form \( \ddot{\Phi} =2E-U \) (where \( \Phi \) is the Jacobi’s function; E and U are the total and potential energy, respectively). In addition, the inner and outer force fields and the energy as the measure of interacted mass particles of a celestial body were revealed. The reduced inner gravitational (weighting) field was obtained.


Mass Point Celestial Body Hydrostatic Equilibrium Virial Theorem Polar Moment 
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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • V. I. Ferronsky
    • 1
  • S. V. Ferronsky
  1. 1.Water Problems Institute of the Russian Academy of SciencesMoscowRussia

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