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<H2><A NAME="SECTION0004115000000000000000">SLA_MAPQK - Quick Mean to Apparent</A>
<A NAME="xref_SLA_MAPQK"> </A><A NAME="SLA_MAPQK"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Quick mean to apparent place: transform a star <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> from
mean place to geocentric apparent place, given the
star-independent parameters. The reference frames and
timescales used are post IAU 1976.
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_MAPQK (RM, DM, PR, PD, PX, RV, AMPRMS, RA, DA)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RM,DM</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>mean <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>PR,PD</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>proper motions: <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> changes per Julian year</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PX</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>parallax (arcsec)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RV</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>radial velocity (km s<SUP>-1</SUP>, +ve if receding)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>AMPRMS</EM></TD>
<TD ALIGN="LEFT"><B>D(21)</B></TD>
<TD ALIGN="LEFT" NOWRAP>star-independent mean-to-apparent parameters:</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(1)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>time interval for proper motion (Julian years)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(2-4)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>barycentric position of the Earth (AU)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(5-7)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>heliocentric direction of the Earth (unit vector)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(8)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>(gravitational radius of
Sun)<IMG WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img16.gif"
ALT="$\times 2 / $">(Sun-Earth distance)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(9-11)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP><B>v</B>: barycentric Earth velocity in units of c</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(12)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP><IMG WIDTH="72" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
SRC="img17.gif"
ALT="$\sqrt{1-\left\vert\mbox{\bf v}\right\vert^2}$"></TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(13-21)</TD>
<TD></TD>
<TD ALIGN="LEFT" NOWRAP>precession/nutation <IMG WIDTH="39" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img18.gif"
ALT="$3\times3$"> matrix</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RA,DA</EM></TD>
<TH ALIGN="LEFT"><B>D </B></TH>
<TD ALIGN="LEFT" NOWRAP>apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> (radians)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>Use of this routine is appropriate when efficiency is important
and where many star positions, all referred to the same equator
and equinox, are to be transformed for one epoch. The
star-independent parameters can be obtained by calling the
sla_MAPPA routine.
<DT>2.
<DD>If the parallax and proper motions are zero the sla_MAPQKZ
routine can be used instead.
<DT>3.
<DD>The vectors AMPRMS(2-4) and AMPRMS(5-7) are referred to
the mean equinox and equator of epoch EQ.
<DT>4.
<DD>Strictly speaking, the routine is not valid for solar-system
sources, though the error will usually be extremely small.
However, to prevent gross errors in the case where the
position of the Sun is specified, the gravitational
deflection term is restrained within about <IMG WIDTH="33" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img124.gif"
ALT="$920\hspace{-0.05em}^{'\hspace{-0.1em}'}$"> of the
centre of the Sun's disc. The term has a maximum value of
about
<IMG WIDTH="31" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img125.gif"
ALT="$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.85$"> at this radius, and decreases to zero as
the centre of the disc is approached.
</DL></DL>
<P> <DL>
<DT><STRONG>REFERENCES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>1984 <I>Astronomical Almanac</I>, pp B39-B41.
<DT>2.
<DD>Lederle & Schwan, 1984. <I>Astr.Astrophys.</I> <B>134</B>, 1-6.
</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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