![]() ![]() In principle this can be done using three reference stars of known position to determine the six unknown quantities. The constant coefficients a, b, c, d, e and f are to be determined for each image. The symbols (X,Y) and (x,y) have the meanings given above. The transformation equations are as follows: ![]() The first step is to determine the transformation between image and standard coordinates. Transformation From Image to Celestial Coordinates The transformation equations are given below. Once that has been done, the standard coordinates for any object can be converted to RA and DEC using straightforward spherical trigonometry. The usual way this is done is to assume a simple linear transformation between the standard coordinates and the image coordinates, and to determine the coefficients for that transformation. The trick of astrometry is to turn your image coordinates into celestial coordinates. Ideally the (x,y) and (X,Y) coordinates would be the same. These differ from standard coordinates because of things like tilt or rotation of the CCD, and also because of possible optical distortions. Image Coordinates (x,y) These are the x-y coordinates of an object in your image measured in pixels from the image center (could be in mm if you are using a photograph rather than a CCD image).The origin of the standard system is at the tangent point in the image. The X coordinate is aligned with RA and the Y coordinate is aligned with DEC. Standard Coordinates (X,Y) These are the projection of the RA and DEC of an object onto the tangent plane of the sky, i.e., the plane tangent to the sphere of the sky that intersects the sky at the tangent point (which is usually somewhat offset from the image center).These are probably what you would like to determine for the objects you are observing. Celestial Coordinates (RA,DEC) These are the normal RA and DEC of the Celestial Coordinate system.Our treatment follows that found in HAIP, though leaving out much detail. Some will be familiar, some will likely be new. There are several different coordinate systems we will use in determining our object coordinates. In addition, most software packages can interact with these catalogs to determine positions of objects in CCD images. They are listed at the bottom of this page. In fact, these catalogs have been compiled just for this purpose. ![]() Fortunately, several star catalogs exist that are suitable for astrometric use. Assuming such a set of objects with known coordinates exists, you can in principle put any unknown objects on the same coordinate system as the know objects. The basic idea behind astrometry is to determine the unknown coordinates of objects by comparing their location on an image to the location of a set of objects on the same image whose coordinates are already determined. For a more substantial treatment of the background of some of the methods described, see The Handbook of Astronomical Image Processing (HAIP). Here we outline the basic steps you will have to go through in order to obtain accurate positions for objects in your fields. Modern CCD images and analysis software are able to produce positions accurate to better than one arcsecond when suitable catalogs of comparison objects are used. If you're thinking of coming to one of our viewing events, its always a good idea to check the club's email list for last minute updates.Astrometry is the process of determining positions of objects in your field. We may randomly do sidewalk astronomy around the area, as well as occasional school and camp groups. Various of our club members volunteer to provide a viewing experience to the public. We hold a monthly 'star party' at Quail Hollow Ranch County Park, starting about sunset (its fully dark typically 90 minutes after sunset) as weather allows. We meet on the Second Wednesday of every month at 7:00pm, at the Santa Margarita Meeting Room at the Scotts Valley Water District Offices, and hold several star parties per month. Our emphasis is telescope observing, family participation, and public enjoyment of the wonders of the starry night. The Santa Cruz Astronomy Club serves all communities in Santa Cruz County, California and neighboring areas. ![]()
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