Astrometric calculation procedure

This calculator computes the sky coordinates (RA, Dec) of an object in your image (e.g., an asteroid), given the known coordinates of a set of stars in the image. You supply the known RA,Dec of a set of stars in the image, the x,y pixel coordinates of those stars, and the x,y pixel coordinates of the object.

The calculator first determines the so-called "plate constants" --- parameters in a transformation between x,y image pixel coordinates and RA,Dec sky coordinates determined from the star information you entered. The name "plate constants" comes from when this procedure was done with images obtained on photographic plates. The plate constants are determined by a "least-squares fit" of the transformation equations to the star data you enter. The plate constants a,b,c,d,e,f are output in case you're interested in seeing what their values look like.

The actual transformation equations are

u = x + ax + by + c
v = y + dx + ey + f

where u,v are angular sky coordinates (related to RA, Dec) measured relative to the center of the image and x,y are pixel coordinates in the image. For more information on this astrometric reduction procedure see, for example, "How to Reduce Plate Measurements," by Brian G. Marsden, in Sky & Telescope magazine (September 1982, page 284), and "Measuring Positions on a Photograph," by Jordon D. Marche, also in Sky & Telescope (July 1990, page 71).

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