Within the 1979-1982 time frame, at Delft University's Department of Aerospace Engineering some numerical experiments were performed by processing a limited number of multiday global tracking data arcs. Each arc consisted of laser ranging data acquired in the 1978-1980 period. These arcs were selected especially for their relative abundance of European observations of the satellites LAGEOS, Starlette, and GEOS 3. An evaluation of the orbit errors due to errors in the gravity models was performed both in terms of apparent range and timing biases of each pass over a tracking station and of orbit differences between solutions in which different gravity models were applied. In addition, from LAGEOS and Starlette tracking data, separate solutions were obtained for the positions of the European laser ranging stations at Kootwijk, Wettzell, Grasse, and Mets/ihovi. In spite of the use of the most accurate tailored gravity models available at the time, the results, both in terms of absolute coordinates and in baselines, often differ considerably from more recent solutions by other authors. It is hypothesized that intermittent data-taking problems at some of the European stations are responsible for these differences. Their distorting effects are relatively strong because of the limited number of passes on which our solutions are based. INTRODUCTIONAlthough the use of space geodetic techniques may have a variety of objectives, accurate spatial positioning of terrestrial points in a regional to global context should be regarded a fundamental one. Depending on the accuracy achieved, the results have a wide scope of applications, covering from general surveying to the monitoring of crustal movements. Groundbased laser ranging to artificial satellites is as yet the most precise technique for station-to-satellite relative positioning. This is ultimately due to the excellent predictability of atmospheric effects on light travel time. Because of this feature, ground-based satellite laser ranging (SLR) in conjuntion with dedicated satellites is considered a promising tool for accurate relative positioning of stations as a contribution to investigations of lithospheric plate motions and deformation.The Observatory for Satellite Geodesy at Kootwijk, The Netherlands, has from 1976 onward successfully laser ranged several of the available retroreflecting satellites. Together with laser range observations from other stations, obtained as a result of data exchange arrangements, Kootwijk data collected in the course of time are analyzed primarily for relative station position recovery. This is done in a cooperative effort by the Section Orbital Mechanics of the Delft University of Technology's Department of Aerospace Engineering and the Observatory for Satellite Geodesy. Their investigations do not only aim at the determination of relative positions of SLR stations but also at an assessment of the accuracy of such determinations. This is regarded as of critical importance in view of the ultimate objective of the relative positioning: the...

The geometric approach to satellite geodesy through simultaneous observations is discussed in general and as regards pure simultaneous ranging to a satellite in some detail. Closed expressions are derived for the geometric conditions imposed upon a network of satellite tracking stations joining in simultaneous ranging. The mathematical procedure suggested is symmetric in all stations and only involves the unknown distances between them and the measured ranges to a satellite. A comparison is made with similar 1-and 2-dimensional problems.

The earth's external gravitational potential may be mathematically expressed as an infinite series of spherical harmonics. The coefficients in such series depend numerically on the location and orientation of the adopted system of reference with respect to the body of the earth. The present subject is to derive general formulae for the numerical changes of the harmonic coefficients due to both a re-orientation and a re-location of the reference frame. Such formulae could be of value in critical studies of the impact of artificial satellites on dynamical geodesy, especially when combining the results with those from terrestrial geodesy. Use has been made of a transformation property of spherical harmonics which seems to be not a part of standard mathematics. Some simple numerical examples are given. ( n -S ) ! 1 ( n + s)! Ma" IM Ji=cE,--__ r" cossl . Pi(sinp)dm.Here GM stands for the product of the universal constant of gravitation G and the total mass M of the earth; the mass of the atmosphere will be neglected. a is an arbitrary scaling factor which conveniently can be taken as to coincide with the equatorial radius of the earth. r, 1 and ( =latitude) are the conventional spherical coordinates and the notation of the associated Legendre functions of the first kind could follow Hobson (1931): 1 if s = O 2 if s>O. (?a + a)! Tellus XXI (1969), 4

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