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<H2><A NAME="SECTION000410000000000000000">SLA_AOPQK - Quick Appt-to-Observed</A>
<A NAME="xref_SLA_AOPQK"> </A><A NAME="SLA_AOPQK"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Quick apparent to observed place (but see Note 8, below).
<DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_AOPQK (RAP, DAP, AOPRMS, AOB, ZOB, HOB, DOB, ROB)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RAP,DAP</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>geocentric apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>AOPRMS</EM></TD>
<TD ALIGN="LEFT"><B>D(14)</B></TD>
<TD ALIGN="LEFT" NOWRAP>star-independent apparent-to-observed parameters:</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(1)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>geodetic latitude (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(2,3)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>sine and cosine of geodetic latitude</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(4)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>magnitude of diurnal aberration vector</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(5)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>height (metres)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(6)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>ambient temperature (degrees K)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(7)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>pressure (mB)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(8)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>relative humidity (0-1)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(9)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>wavelength (<IMG WIDTH="26" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img21.gif"
ALT="$\mu{\rm m}$">)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(10)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>lapse rate (degrees K per metre)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(11,12)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>refraction constants A and B (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(13)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>longitude + eqn of equinoxes +
``sidereal <IMG WIDTH="16" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img19.gif"
ALT="$\Delta$">UT'' (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(14)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>local apparent sidereal time (radians)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>AOB</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>observed azimuth (radians: N=0, E=<IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img22.gif"
ALT="$90^{\circ}$">)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ZOB</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>observed zenith distance (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>HOB</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>observed Hour Angle (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DOB</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>observed Declination (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ROB</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>observed Right Ascension (radians)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>This routine returns zenith distance rather than elevation
in order to reflect the fact that no allowance is made for
depression of the horizon.
<DT>2.
<DD>The accuracy of the result is limited by the corrections for
refraction. Providing the meteorological parameters are
known accurately and there are no gross local effects, the
predicted azimuth and elevation should be within about
<P> <IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img25.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$"> for <IMG WIDTH="56" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img26.gif"
ALT="$\zeta<70^{\circ}$">. Even
at a topocentric zenith distance of
<IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img22.gif"
ALT="$90^{\circ}$">, the accuracy in elevation should be better than
1 arcminute; useful results are available for a further
<IMG WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img27.gif"
ALT="$3^{\circ}$">, beyond which the sla_REFRO routine returns a
fixed value of the refraction. The complementary
routines sla_AOP (or sla_AOPQK) and sla_OAP (or sla_OAPQK)
are self-consistent to better than 1 microarcsecond all over
the celestial sphere.
<DT>3.
<DD>It is advisable to take great care with units, as even
unlikely values of the input parameters are accepted and
processed in accordance with the models used.
<DT>4.
<DD><I>Apparent</I> <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> means the geocentric apparent right ascension
and declination, which is obtained from a catalogue mean place
by allowing for space motion, parallax, precession, nutation,
annual aberration, and the Sun's gravitational lens effect. For
star positions in the FK5 system (<I>i.e.</I> J2000), these effects can
be applied by means of the sla_MAP <I>etc.</I> routines. Starting from
other mean place systems, additional transformations will be
needed; for example, FK4 (<I>i.e.</I> B1950) mean places would first
have to be converted to FK5, which can be done with the
sla_FK425 <I>etc.</I> routines.
<DT>5.
<DD><I>Observed</I> <IMG WIDTH="66" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img28.gif"
ALT="$[\,Az,El~]$"> means the position that would be seen by a
perfect theodolite located at the observer. This is obtained
from the geocentric apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> by allowing for Earth
orientation and diurnal aberration, rotating from equator
to horizon coordinates, and then adjusting for refraction.
The <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img29.gif"
ALT="$[\,h,\delta\,]$"> is obtained by rotating back into equatorial
coordinates, using the geodetic latitude corrected for polar
motion, and is the position that would be seen by a perfect
equatorial located at the observer and with its polar axis
aligned to the Earth's axis of rotation (<I>n.b.</I> not to the
refracted pole). Finally, the <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img24.gif"
ALT="$\alpha$"> is obtained by subtracting
the <I>h</I> from the local apparent ST.
<DT>6.
<DD>To predict the required setting of a real telescope, the
observed place produced by this routine would have to be
adjusted for the tilt of the azimuth or polar axis of the
mounting (with appropriate corrections for mount flexures),
for non-perpendicularity between the mounting axes, for the
position of the rotator axis and the pointing axis relative
to it, for tube flexure, for gear and encoder errors, and
finally for encoder zero points. Some telescopes would, of
course, exhibit other properties which would need to be
accounted for at the appropriate point in the sequence.
<DT>7.
<DD>The star-independent apparent-to-observed-place parameters
in AOPRMS may be computed by means of the sla_AOPPA routine.
If nothing has changed significantly except the time, the
sla_AOPPAT routine may be used to perform the requisite
partial recomputation of AOPRMS.
<DT>8.
<DD>The ``sidereal <IMG WIDTH="16" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img19.gif"
ALT="$\Delta$">UT'' which forms part of AOPRMS(13)
is UT1-UTC converted from solar to
sidereal seconds and expressed in radians.
<DT>9.
<DD>At zenith distances beyond about <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img33.gif"
ALT="$76^\circ$">, the need for
special care with the corrections for refraction causes a
marked increase in execution time. Moreover, the effect
gets worse with increasing zenith distance. Adroit
programming in the calling application may allow the
problem to be reduced. Prepare an alternative AOPRMS array,
computed for zero air-pressure; this will disable the
refraction corrections and cause rapid execution. Using
this AOPRMS array, a preliminary call to the present routine
will, depending on the application, produce a rough position
which may be enough to establish whether the full, slow
calculation (using the real AOPRMS array) is worthwhile.
For example, there would be no need for the full calculation
if the preliminary call had already established that the
source was well below the elevation limits for a particular
telescope.
<DT>10.
<DD>The azimuths <I>etc.</I> used by the present routine are with
respect to the celestial pole. Corrections to the terrestrial pole
can be computed using sla_POLMO.
</DL></DL>
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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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