Astrometric plate reductions with orthogonal functions
Abstract
Approximately orthogonal polynomials were used to evaluate the relations between standard and plate coordinates of the same star, and the formalism was applied to six plates of the Pleiades and Praesepe obtained with the Greenwich astrograph. The results were compared with those of Brosche and Geffert (1988) obtained on the same plates using ordinary polynomials. It was found that, provided that normalized variables are used in all cases, the advantages of orthogonal functions occur if, and only if, the highest order of significant functions in one of the arguments is larger than 1. In the latter case, ordinary polynomials lead to corelated plate constants with larger errors (e.g., the errors of the plate scales were typically 20 percent larger than for the orthogonal model).
 Publication:

Astronomy and Astrophysics
 Pub Date:
 February 1989
 Bibcode:
 1989A&A...211..239B
 Keywords:

 Astrometry;
 Astronomical Models;
 Orthogonal Functions;
 Photographic Plates;
 Stars;
 Astrography;
 Astronomical Catalogs;
 Error Analysis;
 Astronomy