Quaternions as Astrometric Plate Constants
Abstract
A new method for solving problems in relative astrometry is proposed. In it, the relationship between the measured quantities and the components of the position vector of a star is modeled using quaternions, in effect replacing the plate constants of a standard fourplateconstant solution with the four components of a quaternion. The method allows a direct solution for the position vectors of the stars, and hence for the equatorial coordinates. Distortions, magnitude, and color effects are readily incorporated into the formalism, and the method is directly applicable to overlappingplate problems. The advantages of the method include the simplicity of the resulting equations, their freedom from singularities, and the fact that trigonometric functions and tangential point transformations are not needed to model the plate material. A global solution over the entire sky is possible.
 Publication:

The Astronomical Journal
 Pub Date:
 March 1987
 DOI:
 10.1086/114359
 Bibcode:
 1987AJ.....93..755J
 Keywords:

 Astrometry;
 Photographic Plates;
 Quaternions;
 Coordinates;
 Position (Location);
 Stellar Color;
 Stellar Magnitude;
 Astronomy;
 ANALYTICAL METHODS