Fys M. Mathematical models of the density distribution of the planets and their gravitational fields

The thesis is devoted to developing methods for description of the internal structure and gravitational fields of the planets. It was constructed, a system of harmonic functions in an ellipsoid. We give a view of potential by everywhere convergent series. A new approach to the use of Stokes constant is proposed and considering it the limits of variation value of the density in the center of the planet, formulas for density calculating and internal potential of some distributions were obtained. The methods for investigating of state of hydrostatic equilibrium of planets and for approximation of piecewise continuous mass distribution, which determines internal potential and the value of the gravitational energy of celestial bodies were proposed.