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<H2><A NAME="SECTION0004123000000000000000">SLA_OAPQK - Quick Observed to Apparent</A>
<A NAME="xref_SLA_OAPQK"> </A><A NAME="SLA_OAPQK"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Quick observed to apparent place.
<DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_OAPQK (TYPE, OB1, OB2, AOPRMS, RAP, DAP)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>TYPE</EM></TD>
<TH ALIGN="LEFT"><B>C*(*)</B></TH>
<TD ALIGN="LEFT" NOWRAP>type of coordinates - `R', `H' or `A' (see below)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>OB1</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>observed Az, HA or RA (radians; Az is 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>OB2</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>observed zenith distance or <IMG WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img23.gif"
ALT="$\delta$"> (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 (HM)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(6)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>ambient temperature (TDK)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(7)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>pressure (PMB)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(8)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>relative humidity (RH)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(9)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>wavelength (WL)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(10)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>lapse rate (TLR)</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>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="$[\,\alpha,\delta\,]$"></TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>Only the first character of the TYPE argument is significant.
`R' or `r' indicates that OBS1 and OBS2 are the observed Right
Ascension and Declination; `H' or `h' indicates that they are
Hour Angle (west +ve) and Declination; anything else (`A' or
`a' is recommended) indicates that OBS1 and OBS2 are Azimuth
(north zero, east is <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img22.gif"
ALT="$90^{\circ}$">) and Zenith Distance. (Zenith
distance is used 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>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
related to the observed <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img29.gif"
ALT="$[\,h,\delta\,]$"> via the standard rotation, using
the geodetic latitude (corrected for polar motion), while the
observed HA and RA are related simply through the local
apparent ST. <I>Observed</I> <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> or <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img29.gif"
ALT="$[\,h,\delta\,]$"> thus means 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).
By removing from the observed place the effects of
atmospheric refraction and diurnal aberration, the
geocentric apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> is obtained.
<DT>5.
<DD>Frequently, <I>mean</I> rather than <I>apparent</I>
<IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> will be required,
in which case further transformations will be necessary. The
sla_AMP <I>etc.</I> routines will convert
the apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> produced
by the present routine into an FK5 J2000 mean place, by
allowing for the Sun's gravitational lens effect, annual
aberration, nutation and precession. Should FK4 B1950
coordinates be needed, the routines sla_FK524 <I>etc.</I> will also
need to be applied.
<DT>6.
<DD>To convert to apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> the coordinates read from a
real telescope, corrections would have to be applied for
encoder zero points, gear and encoder errors, tube flexure,
the position of the rotator axis and the pointing axis
relative to it, non-perpendicularity between the mounting
axes, and finally for the tilt of the azimuth or polar axis
of the mounting (with appropriate corrections for mount
flexures). 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 azimuths <I>etc.</I> used by the present routine are with
respect to the celestial pole. Corrections from 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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