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An algorithm for the (kinematic) orbit analysisof a Low Earth Orbiting (LEO) GPS tracked satellite to determinethe spherical harmonic coefficients of the terrestrialgravitational field is presented. A contribution to existinglong wavelength gravity field models is expected since thekinematic orbit of a LEO satellite can nowadays be determinedwith very high accuracy in the range of a few centimeters.To demonstrate the applicability of the proposedmethod, first results from the analysis of real CHAMP RapidScience (dynamic) Orbits (RSO) and kinematic orbits areillustrated. In particular, we take advantage of Newton’sLaw of Motion which balances the acceleration vector andthe gradient of the gravitational potential with respect to anInertial Frame of Reference (IRF). The satellite’s accelerationvector is determined by means of the second order functionalof Newton’s Interpolation Formula from relative satelliteephemeris (baselines) with respect to the IRF. Thereforethe satellite ephemeris, which are normally given ina Body fixed Frame of Reference (BRF) have to be transformedinto the IRF. Subsequently the Newton interpolatedaccelerations have to be reduced for disturbing gravitationaland non-gravitational accelerations in order to obtain the accelerationscaused by the Earth’s gravitational field. For afirst insight in real data processing these reductions havebeen neglected. The gradient of the gravitational potential,conventionally expressed in vector-valued spherical harmonicsand given in a Body Fixed Frame of Reference, must betransformed from BRF to IRF by means of the polar motionmatrix, the precession-nutation matrices and the GreenwichSiderial Time Angle (GAST). The resulting linear system ofequations is solved by means of a least squares adjustmentin terms of a Gauss-Markov model in order to estimate thespherical harmonics coefficients of the Earth’s gravitationalfield.  <b>Key words.</b> space gravity spectroscopy, spherical harmonicsseries expansion, GPS tracked LEO satellites, kinemati

advances in geosciences

Space Gravity Spectroscopy - determination of the Earth’s gravitational field by means of Newton interpolated LEO ephemeris Case studies on dynamic (CHAMP Rapid Science Orbit) and kinematic orbits