Equinox keyword

[Stupendous Man <richmond@a188-l009.rit.edu>]

   Let me try to explain the meaning of the "Equinox" and "Epoch" 
keywords.  Both refer to the coordinates of astronomical sources.
There are two factors which complicate the description of the
location of star in the sky.

   1) The entire night sky appears to move, very slowly, due to 
      a wobble in the Earth's rotation.  The axis of rotation of
      the Earth currently points in a particular direction, which
      happens to lie in the direction of Polaris.  Just like a
      spinning top, however, the Earth wobbles slightly.  Over
      a period of 26,000 years, the Earth's axis will describe
      a circle of radius 23.5 degrees.  This is called "precession
      of the equinoxes."
 
      As a result, the positions of all the stars in the sky will
      _together_ appear to shift over this 26,000 year period.
      Polaris, for example, which is currently very close to the 
      North Celestial Pole, will be about 57 degrees away from
      the North Celestial Pole in 13,000 years.

      Astronomers use the term "Equinox" to label the date when
      a star's catalogued (RA, Dec) would match the ACTUAL (RA, Dec)
      on the sky.  Many galaxies have positions which are measured
      in the system of "Equinox 1950".  If you look up their 
      tabulated (RA, Dec), you must make a small correction for the
      motion of the Earth's axis since 1950 to the current date.
     
   2) Individual stars are moving through space; they are all orbiting
      around our Milky Way's center, but some go faster than others,
      and in slightly different directions.  As a result, if we watch
      a particular (nearby) star over a period of several years, we
      can see it move relative to other stars.  This is called 
      "proper motion."  

      Note that proper motion causes _individual stars_ to move 
      by differerent amounts -- unlike precession of the equinoxes,
      which causes all the stars in a particular portion of the sky
      to move as a unit.  

      Astronomers use the term "Epoch" to label the date when a
      star's catalogued particular (RA, Dec) was correct.  If one
      looks at the star at a different time, one must correct the
      tabulated position for the distance the star has moved in
      the intervening time.  For example, if a particular star's
      position is given as "Epoch 1980.0", and it's currently 2001,
      then we have to
 
            a) look up the star's proper motion; perhaps we find
               it to be 
                           0.01 arcsec/year in RA
                          -0.03 arcsec/year in Dec

            b) multiply the proper motion by the time elapsed since
               Epoch 1980 (i.e. 21 years)

                           0.21 arcsec in RA
                          -0.69 arcsec in Dec

            c) add these amounts to the star's catalogued position
               to find its current position

  
  Okay, now, what does all this have to do with FITS headers of 
TASS Mark IV images?

  In one sense, nothing.  The Mark IV images are not catalogs.
As long as one knows the date when the image was taken (which is
described by other FITS keywords), then one can make all the necessary
corrections to any positions derived from the Mark IV image.

  In another sense, a tiny bit.  We are trying to place the rough
location (RA, Dec) of the image into the FITS header, as the 
"CRVAL1" and "CRVAL2" keywords.  This (RA, Dec) location is a 
coordinate, so, to some extent, it needs an Equinox.  

  However, to my mind, this is silly.  Currently, Tom is making
a rough estimate of the position to which the camera points: the
precision is a quarter of a degree or so.  This is much larger than
the corrections one would make for precession of the equinoxes,
unless one were looking at the images centuries from now.  
It would be perfectly safe to put

      EQUINOX =    2000.0          /   it's just a rough guess

into the headers, if you really want to put it in.  Strictly speaking,
if Tom is using "Fred's Star Atlas" to figure out the direction
in which the camera is pointing, he should use the Equinox of
positions used in "Fred's Star Atlas."  But I think it really 
doesn't matter.

  I can't see any reason to insert "Epoch", since the (RA, Dec)
in the header does not pertain to a single object with a well-defined
proper motion.  

  If one were to create lists of stars based on the images,
and if one were to place those lists of stars into a FITS table,
_then_ there would be a reason to put 

      EQUINOX =   1997.6          /   if astrometry based on Tycho positions
      EPOCH   =   2001.25         /   based on date when image was taken

into the header of the FITS table.  But until that point, 
these keywords aren't needed.

  In my opinion.

                                       Michael Richmond