Abstract. We present an outline of a new reduction of the Hipparcos astrometric data, the justifications of which are described in the accompanying paper. The emphasis is on those aspects of the data analysis that are fundamentally different from the ones used for the catalogue published in 1997. The new reduction uses a dynamical modelling of the satellite's attitude. It incorporates provisions for scan-phase discontinuities and hits, most of which have now been identified. Solutions for the final along-scan attitude (the reconstruction of the satellite's scan phase), the abscissa corrections and the instrument model, originally solved simultaneously in the great-circle solution, are now de-coupled. This is made possible by starting the solution iterations with the astrometric data from the published catalogue. The de-coupling removes instabilities that affected great-circle solutions for short data sets in the published data. The modelling-noise reduction implies smaller systematic errors, which is reflected in a reduction of the abscissa-error correlations by about a factor 40. Special care is taken to ensure that measurements from both fields of view contribute significantly to the along-scan attitude solution. This improves the overall connectivity of the data and rigidity of the reconstructed sky, which is of critical importance to the reliability of the astrometric data. The changes in the reduction process and the improved understanding of the dynamics of the satellite result in considerable formal-error reductions for stars brighter than 8th magnitude.

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Four widely used algorithms for the computation of the Earth's gravitational potential and its first-, second- and third-order gradients are examined: the traditional increasing degree recursion in associated Legendre functions and its variant based on the Clenshaw summation, plus the methods of Pines and Cunningham--Metris, which are free from the singularities that distinguish the first two methods at the geographic poles. All four methods are reorganized with the lumped coefficients approach, which in the cases of Pines and Cunningham-Metris requires a complete revision of the algorithms. The characteristics of the four methods are studied and described, and numerical tests are performed to assess and compare their precision, accuracy, and efficiency. In general the performance levels of all four codes exhibit large improvements over previously published versions. From the point of view of numerical precision, away from the geographic poles Clenshaw and Legendre offer an overall better quality. Furthermore, Pines and Cunningham--Metris are affected by an intrinsic loss of precision at the equator and suffer from additional deterioration when the gravity gradients components are rotated into the East-North-Up topocentric reference system

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This contribution deals with the derivation of explicit expressions of the gradients of first, second and third order of the gravitational potential. This is accomplished in the framework of tensor analysis which naturally allows to apply general formulae to the specific coordinate systems in use in geodesy. In particular it is recalled here that when the potential field is expressed in general coordinates on a 3D manifold, the gradient operation leads to the definition of the covariant derivative and that the covariant derivative of a tensor can be obtained by application of a simple rule. When applied to the gravitational potential or to any of its gradients, the rule straightforwardly provides the expressions of the higher-order gradients. It is also shown that the tensor approach offers a clear distinction between natural and physical components of the gradients. Two fundamental reference systems---a global, bodycentric system and a local, topocentric system, both body-fixed---are introduced and transformation rules are derived to convert quantities between the two systems. The results include explicit expressions for the gradients of the first three orders in both reference systems

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Portal del coneixement obert de la UPC http://upcommons.upc.edu/e-prints Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Acta astronautica.