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
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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