Current adjustment of the mean Earth ellipsoid parameters

The need for the determination of the parameters of an equipotential rotational ellipsoid of revolution that approximates closer and closer to the Earth requires analysis of the most currently available data. The main objective of this study is to examine such new data and to perform an adjustment technique to estimate the parameters and their standard deviations of the mean Earth ellipsoid. The parameters considered are the geocentric gravitational constant, the angular velocity, the geoidal potential, the dynamical form factor, and the major and minor semi-axes. A-priori estimates of these quantities, which may be determined independently, are treated as “observations” and their adjusted values from a weighted least-squares procedure are presented. Since a level ellipsoid of revolution and its gravity field are completely determined by four constants, we use two non-linear condition equations to relate the six parameters for performing the adjustment. Among the products of the adjustment is the correlation matrix of the adjusted values of parameters, which helps us in the selection of a consistent set of four parameters for the definition of a new Geodetic Reference System (GRS). After the selection of the four parameters, we compute by Newton’s method the two derived parameters and estimate their standard deviations by applying the law of propagation of variances. Furthermore, all the derived geometric and physical constants are computed from the defining constants of a GRS, by means of closed formulas. Finally, in order to yield numerical results of high precision, all computations are executed in computer algebra system software using variable precision floating point numbers.