Astrometry of Fundamental Catalogues The Evolution from Optical to R
Celestial fundamental catalogues are a prerequisite for the determination of absolute positions and motions in space. Presently, positional astrometry is at the watershed between classical fundamental catalogues, based on moving reference stars, and moder
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'STROPHYSICS LIBRARY L Appenzeller, Heidelberg, Germany G. Bomer, Garc hing, Germany M. Harwit, Washi ngto n, DC, USA R. Kippenhahn, Gottingen, Germany J. Lequeux, Paris, France P. A. Strittmatter, Tucson, AZ, USA V. Trimble, College Park, MD, and Irvine, CA, USA
Springer-Verlag Berlin Heidelberg GmbH Physics and Astronomy
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http://www.sp ri nger.de/phys/
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tS 0, but unknown, the relative abscissae of the stars on the RGC reflect a change by the parallactic displacement of the base star in addition to the possible shift due to the choice of the base star position. Both cases give rise to a constant offset in each of all the abscissae pertaining to an individual RGC . This fact , however, does not pose a serious problem because the offsets are constant per RGC and, therefore, can be estimated in a simultaneous solution together with the astrometric parameters, including the parallaxes of all primary stars, i.e. also those of negligible parallaxes. This estimation process uses the abscissae of the entire set of RGCs. Since all 0828+493
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3.7 Sphere Solution
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RGCs are involved one speaks of a global solution at whose completion the constant offsets are known. In anticipating the global solution, these offsets may be eliminated from the abscissae, yielding reduced abscissae that reflect the genuine astrometrically relevant information on stellar position, motion and parallactic displacement, which is the input for astrometric parameter determination that provides absolute parallaxes as one specific result. Section 3.7 discusses the global solution and parameter determination.
3.7 Sphere Solution 3.7.1 Conceptual Background One-dimensional measurements along the scanning direction of the telescope yielded the abscissae of the stars on the respective RGCs. On average a star appeared on 28 RGCs during the 37 months of data acquisition from the satellite. Altogether there are 2281 RGCs, with each of these forming a specific spherical reference frame defined by the fundamental plane of the RGC containing a zero point. The distance between any two stars projected onto an RGC is invariant to changes of the zero point. It is the aim of the 'Sphere Solution' to derive a two-dimensional solution of spherical stellar coordinates from the one-dimensional abscissae measured on RGCs with different poles, and to embed these coordinates into a coherent net on the sphere. The last requirement necessitates the solution of the problem on a global basis rather than on a star-by-star basis. First let us consider an idealized thought experiment to focus on the crucial points of the sphere solution. We assume fixed positions in ecliptic longitude (,\) and latitude (13) of the stars during the observation campaign. Further, the abscissa
