The Effect of Dissipative Moments Caused by Liquid Body Viscosity on the Rotation Stability of a Space Object

The influence of dissipative forces in a viscous liquid that completely fills the cavities of a space object executing a rotational motion is analyzed. The Navier–Stokes equations are solved by expanding them into a series in terms of eigenfunctions of the boundary value problem on involving the resting liquid in rotation around the longitudinal axis of a cavity. The analytical solutions for coaxial cylindrical and concentric spherical cavities are obtained, in particular, for a straight circular cylinder and a sphere. The stability of the single-axis orientation of a space object filled with a viscous liquid is investigated. The dependences of rotation decay processes and drifts of the space object's longitudinal axis from a given direction are shown on the plane of constructive parameters.     

Gravitationally Perturbed Elastic Waves in the Hidden Ocean of Europa

The frequency spectrum of joint hydro-elastic vibrations of the ice surface of the ocean and liquid is analyzed taking into account the proper gravity field of Europa, one of Jupiter’s moons. It is shown how the methods developed for analysis of the vibration stability of earth buildings are used to study seismic properties of the natural Jupiter satellite Europa. Numerical estimates show that when studying the electromagnetic effects and seismic properties of this satellite one should take into account hydro-elastic characteristics due to the closeness of the corresponding frequency spectra.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 3, 2005, pp. 209–214.Original Russian Text Copyright © 2005 by Dokuchaev.     

Spectrum of Natural Vibrations of the Ice Ocean of Jupiter's Moon Europa

The hydroelastic vibrations of the ice surface of the ocean of Europa, a natural satellite of Jupiter, are investigated, and the natural spectrum of frequencies of this surface is determined. The mathematical model of the mechanical system under consideration is presented in the form of a spherical shell, which is wetted by a spherical layer of liquid enveloping a rigid spherical core. The solution of the boundary value problems of the theory of elasticity is sought in the form of expansions into series of the associated Legendre polynomials. It is noted that there are at least three tones of natural vibrations of the shell–spherical liquid layer system, whose periods lie in the vicinity of the ten-hour period of Jupiter's rotation about its axis, and variations of the magnetic field of Europa with the same period.     

On the primordial black holes in the earth

Astrophysical limitations do not exclude the possibility of some number of dark matter primordial Black Holes (BH) being seeded in the interiors of the Earth at the epoch of planet condensation in the young Solar System. We show that limitations on the neutrino radiation due to the BH quantum evaporation and accretion growth of BH mass completely forbid the existence of primordial BH of any mass in the Earth.