On the Determination of Parameters of the Earth’s Figure from Satellite Orbit Dynamics
From observations of perturbations of Earth satellite orbits, various sets of harmonic coefficients have been derived in the development of the gravitational potential of the Earth. If the geocentric constant is given, it is possible, using these quantities, to determine the shape of the equipotential surfaces of the external gravitational potential or of the gravity potential. To determine the dimensions of the surfaces, however, further data would be necessary: the value of the potential on the surface investigated, or the radius-vector of the surface at least in one special case. The paper will be limited to the basic shape characteristics — to the polar and equatorial flattening and the orientation of the equatorial ellipse.
Different ways of determining the “best fitting” parameters are discussed; e.g., under minimum condition of the integral of the squares of Gaussian anomalous curvatures over the whole reference surface, using large sets of harmonics available.
Numerical values obtained: Potential on geoidal surface W0 = 62637.23 × l03m2s-2, scale factor for lengths R0 = 6363675 m, a = 6378138 (mean), α = 1:298.286 (mean polar), α = 1:89000 (mean equatorial).