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+ by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds
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+<TITLE>Different Sorts of Mean Place</TITLE>
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+<H2><A NAME="SECTION000510000000000000000">
+Different Sorts of Mean Place</A>
+</H2>
+A particularly confusing aspect of published mean places is that they
+are sensitive to the precise way they were determined.  A mean
+place is not directly observable, even with fundamental
+instruments such as transit circles, and to produce a mean
+place will involve relying on some existing star catalogue,
+for example the fundamental catalogues FK4 and FK5,
+and applying given mathematical models of precession, nutation,
+aberration and so on.
+Note in particular that no star catalogue,
+even a fundamental catalogue such as FK4 or
+FK5, defines a coordinate system, strictly speaking;
+it is merely a list of star positions and proper motions.
+However, once the stars from a given catalogue
+are used as position calibrators, <I>e.g.</I> for
+transit-circle observations or for plate reductions, then a
+broader sense of there being a coordinate grid naturally
+arises, and such phrases as ``in the system of
+the FK4'' can legitimately be employed.  However,
+there is no formal link between the
+two concepts - no ``standard least squares fit'' between
+reality and the inevitably flawed catalogues.<A NAME="tex2html6" HREF="footnode.html#28038"><SUP><IMG  ALIGN="BOTTOM" BORDER="1" ALT="[*]" SRC="foot_motif.gif"></SUP></A>  All such
+catalogues suffer at some level from systematic, zonal distortions
+of both the star positions and of the proper motions,
+and include measurement errors peculiar to individual
+stars.
+<P>
+Many of these complications are of little significance except to
+specialists.  However, observational astronomers cannot
+escape exposure to at least the two main varieties of
+mean place, loosely called
+FK4 and FK5, and should be aware of
+certain pitfalls.  For most practical purposes the more recent
+system, FK5, is free of surprises and tolerates naive
+use well.  FK4, in contrast, contains two important traps:
+<UL>
+<LI> The FK4 system rotates at about
+<P>      <IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img83.gif"
+ ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$">    per century relative to distant galaxies.
+      This is manifested as a systematic distortion in the
+      proper motions of all FK4-derived catalogues, which will
+      in turn pollute any astrometry done using those catalogues.
+      For example, FK4-based astrometry of a QSO using plates
+      taken decades apart will reveal a non-zero <I>fictitious proper
+      motion</I>, and any FK4 star which happens to have zero proper
+      motion is, in fact, slowly moving against the distant
+      background.  The FK4 frame rotates because it was
+      established before the nature of the Milky Way, and hence the
+      existence of systematic motions of nearby stars, had been
+      recognized.
+<LI> Star positions in the FK4 system are part-corrected for
+      annual aberration (see above) and embody the so-called
+      E-terms of aberration.
+</UL>
+The change from the old FK4-based system to FK5
+occurred at the beginning
+of 1984 as part of a package of resolutions made by the IAU in 1976,
+along with the adoption of J2000 as the reference epoch.  Star
+positions in the newer, FK5, system are free from the E-terms, and
+the system is a much better approximation to an
+inertial frame (about five times better).
+<P>
+It may occasionally be convenient to specify the FK4 fictitious proper
+motion directly.  In FK4, the centennial proper motion of (for example)
+a QSO is:
+<P><IMG WIDTH="56" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
+ SRC="img266.gif"
+ ALT="$\mu_\alpha=-$"><IMG WIDTH="65" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img267.gif"
+ ALT="$0^{\rm s}\hspace{-0.3em}.015869$">+((<IMG WIDTH="65" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img268.gif"
+ ALT="$0^{\rm s}\hspace{-0.3em}.029032$"><IMG WIDTH="56" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
+ SRC="img269.gif"
+ ALT="$~\sin \alpha
+ +$"><IMG WIDTH="65" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img270.gif"
+ ALT="$0^{\rm s}\hspace{-0.3em}.000340$"><IMG WIDTH="98" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img271.gif"
+ ALT="$~\cos \alpha ) \sin \delta
+ -$"><IMG WIDTH="65" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img272.gif"
+ ALT="$0^{\rm s}\hspace{-0.3em}.000105$"><IMG WIDTH="58" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
+ SRC="img273.gif"
+ ALT="$~\cos \alpha
+ -$"><IMG WIDTH="65" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img274.gif"
+ ALT="$0^{\rm s}\hspace{-0.3em}.000083$"><IMG WIDTH="84" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img275.gif"
+ ALT="$~\sin \alpha ) \sec \delta $"> <BR>
+<IMG WIDTH="56" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
+ SRC="img276.gif"
+ ALT="$\mu_\delta\,=+$">      <IMG WIDTH="56" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img277.gif"
+ ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.43549$">   <IMG WIDTH="58" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
+ SRC="img273.gif"
+ ALT="$~\cos \alpha
+ -$">      <IMG WIDTH="56" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img278.gif"
+ ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00510$">   <IMG WIDTH="70" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img279.gif"
+ ALT="$~\sin \alpha +
+ ($">      <IMG WIDTH="56" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img280.gif"
+ ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00158$">   <IMG WIDTH="56" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
+ SRC="img281.gif"
+ ALT="$~\sin \alpha
+ -$">      <IMG WIDTH="56" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img282.gif"
+ ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00125$">   <IMG WIDTH="98" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img271.gif"
+ ALT="$~\cos \alpha ) \sin \delta
+ -$">      <IMG WIDTH="56" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img283.gif"
+ ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.00066$">   <IMG WIDTH="43" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ SRC="img284.gif"
+ ALT="$~\cos \delta $">
+<BR> <HR>
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+<BR> <HR> <P>
+<P><!--End of Navigation Panel-->
+<ADDRESS>
+<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I>
+</ADDRESS>
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