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<H2><A NAME="SECTION000513000000000000000">
Apparent Place to Observed Place</A>
</H2>
The <I>observed place</I> of a source is its position as
seen by a perfect theodolite at the location of the
observer. Transformation of an apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> to observed
place involves the following effects:
<P><UL>
<LI> <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> to <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img29.gif"
ALT="$[\,h,\delta\,]$">.<LI> Diurnal aberration.
<LI> <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img29.gif"
ALT="$[\,h,\delta\,]$"> to <IMG WIDTH="66" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img28.gif"
ALT="$[\,Az,El~]$">.<LI> Refraction.
</UL>
The transformation from apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> to
apparent <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img29.gif"
ALT="$[\,h,\delta\,]$"> is made by allowing for
<I>Earth rotation</I> through the <I>sidereal time</I>, <IMG WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img298.gif"
ALT="$\theta$">:
<P ALIGN="CENTER"><IMG WIDTH="70" HEIGHT="25"
SRC="img299.gif"
ALT="\begin{displaymath}
h = \theta - \alpha \end{displaymath}"></P>
For this equation to work, <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img24.gif"
ALT="$\alpha$"> must be the apparent right
ascension for the time of observation, and <IMG WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img298.gif"
ALT="$\theta$"> must be
the <I>local apparent sidereal time</I>. The latter is obtained
as follows:
<DL COMPACT>
<DT>1.
<DD>from civil time obtain the coordinated universal time, UTC
(more later on this);
<DT>2.
<DD>add the UT1-UTC (typically a few tenths of a second) to
give the UT;
<DT>3.
<DD>from the UT compute the Greenwich mean sidereal time (using
sla_GMST);
<DT>4.
<DD>add the observer's (east) longitude, giving the local mean
sidereal time;
<DT>5.
<DD>add the equation of the equinoxes (using
sla_EQEQX).
</DL>
The <I>equation of the equinoxes</I> (<IMG WIDTH="78" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img300.gif"
ALT="$=\Delta\psi\cos\epsilon$"> plus
small terms)
is the effect of nutation on the sidereal time.
Its value is typically a second or less. It is
interesting to note that if the object of the exercise is to
transform a mean place all the way into an observed place (very
often the case),
then the equation of the
equinoxes and the longitude component of nutation can both be
omitted, removing a great deal of computation. However, SLALIB
follows the normal convention and works <I>via</I> the apparent place.
<P>
Note that for very precise work the observer's longitude should
be corrected for <I>polar motion</I>. This can be done with
sla_POLMO.
The corrections are always less than about
<IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img32.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$"> , and
are futile unless the position of the observer's telescope is known
to better than a few metres.
<P>
Tables of observed and
predicted UT1-UTC corrections and polar motion data
are published every few weeks by the International Earth Rotation Service.
<P>
The transformation from apparent <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img29.gif"
ALT="$[\,h,\delta\,]$"> to <I>topocentric</I>
<IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img29.gif"
ALT="$[\,h,\delta\,]$"> consists of allowing for
<I>diurnal aberration</I>. This effect, maximum amplitude
<IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img76.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$"> ,
was described earlier. There is no specific SLALIB routine
for computing the diurnal aberration,
though the routines
sla_AOP <I>etc.</I> include it, and the required velocity vector can be
determined by calling
sla_GEOC.
<P>
The next stage is the major coordinate rotation from local equatorial
coordinates <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img29.gif"
ALT="$[\,h,\delta\,]$"> into horizon coordinates. The SLALIB routines
sla_E2H
<I>etc.</I> can be used for this. For high-precision
applications the mean geodetic latitude should be corrected for polar
motion.
<P>
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Refraction</A>
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Efficiency considerations</A>
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<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>
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