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authorJoseph Hunkeler <jhunkeler@gmail.com>2015-03-04 21:21:30 -0500
committerJoseph Hunkeler <jhunkeler@gmail.com>2015-03-04 21:21:30 -0500
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+<TITLE>SLA_MAPQK - Quick Mean to Apparent</TITLE>
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+<H2><A NAME="SECTION0004115000000000000000">SLA_MAPQK - Quick Mean to Apparent</A>
+<A NAME="xref_SLA_MAPQK">&#160;</A><A NAME="SLA_MAPQK">&#160;</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&nbsp;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 &amp; Schwan, 1984. <I>Astr.Astrophys.</I> <B>134</B>, 1-6.
+</DL></DL>
+<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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