To Pizzetti's Theory of the Level Ellipsoid

The topic of the Earth's reference body, which has now been established as Pizzetti's level rotational ellipsoid, is analysed. Such a body is fully determined by four parameters: a, GM, J ₂ and . At present, the largest discrepancy in determining these parameters occurs in the value of a, which may in future be replaced by the gravity potential of the mean sea level W _o, with respect to Brovar's condition.Pizzetti's four parameters of the reference body are determined by solving the Dirichlet boundary value problem. The Dirichlet problem has only a unique solution, which, however, can be expressed in infinitely many ways. It turns out that the most important part in the form of the solution is played by Lamé's conditions, which determine the type of ellipsoidal coordinates.The solutions given by Pizzetti, Molodensky and another variant are considered. The last variant leads to a simple formula for the potential of the reference ellipsoid, but the formulae for Lamé's coefficients are inconvenient. Of course, all the methods lead to identical solutions, but some of them are more convenient for the historical use of logarithms, whereas others are more appropriate for use in computers.     

Transformation of the Geodetic Horizontal Control to Another Reference Ellipsoid

Studia Geophysica et Geodaetica -     

Solution to the Stokes Boundary-Value Problem on an Ellipsoid of Revolution

We have constructed Green's function to Stokes's boundary-value problem with the gravity data distributed over an ellipsoid of revolution. We show that the problem has a unique solution provided that the first eccentricity e₀ of the ellipsoid of revolution is less than 0·65041. The ellipsoidal Stokes function describing the effect of ellipticity of the boundary is expressed in the E-approximation as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Stokes function at the singular point = 0. We prove that the degree of singularity of the ellipsoidal Stokes function in the vicinity of its singular point is the same as that of the spherical Stokes function.     

Temporal Variations in Sea Surface Topography and Dynamics of the Earth's Inertia Ellipsoid

Temporal variations in the nine elements of the Earth's inertia ellipsoid due to sea surface topography dynamics were derived from TOPEX/POSEIDON altimeter data 1993 - 1996. The variations amount to about 10 mm in the position of the center of the Earth's inertia ellipsoid (E _i ), 0.15' in the polar axis direction of E _i and to about 0.0003 in the denominator of its polar flattening. The approach used is based on the temporal variations of distortions computed by means of the geopotential model EGM96 which is used as reference.