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+<H2><A NAME="SECTION0004114000000000000000">SLA_MAPPA - Mean to Apparent Parameters</A>
+<A NAME="xref_SLA_MAPPA">&#160;</A><A NAME="SLA_MAPPA">&#160;</A>
+</H2>
+ <DL>
+<DT><STRONG>ACTION:</STRONG>
+<DD>Compute star-independent parameters in preparation for
+conversions between mean place and geocentric apparent place.
+ The parameters produced by this routine are required in the
+ parallax, light deflection, aberration, and precession/nutation
+ parts of the mean/apparent transformations.
+ The reference frames and timescales used are post IAU&nbsp;1976.
+<P> <DT><STRONG>CALL:</STRONG>
+<DD><TT>CALL sla_MAPPA (EQ, DATE, AMPRMS)</TT>
+<P> </DL>
+<P> <DL>
+<DT><STRONG>GIVEN:</STRONG>
+<DD>
+<BR>
+<TABLE CELLPADDING=3>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>EQ</EM></TD>
+<TH ALIGN="LEFT"><B>D</B></TH>
+<TD ALIGN="LEFT" NOWRAP>epoch of mean equinox to be used (Julian)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DATE</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>TDB (JD-2400000.5)</TD>
+</TR>
+</TABLE></DL>
+<P> <DL>
+<DT><STRONG>RETURNED:</STRONG>
+<DD>
+<BR>
+<TABLE CELLPADDING=3>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>AMPRMS</EM></TD>
+<TH ALIGN="LEFT"><B>D(21)</B></TH>
+<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>NOTES:</STRONG>
+<DD><DL COMPACT>
+<DT>1.
+<DD>For DATE, the distinction between the required TDB and TT
+is always negligible. Moreover, for all but the most
+critical applications UTC is adequate.
+ <DT>2.
+<DD>The accuracy of the routines using the parameters AMPRMS is
+ limited by the routine sla_EVP, used here to compute the
+ Earth position and velocity by the methods of Stumpff.
+ The maximum error in the resulting aberration corrections is
+ about 0.3 milliarcsecond.
+ <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>The parameters produced by this routine are used by
+ sla_MAPQK and sla_MAPQKZ.
+ </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>
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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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