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<H2><A NAME="SECTION0004139000000000000000">SLA_PREC - Precession Matrix (FK5)</A>
<A NAME="xref_SLA_PREC"> </A><A NAME="SLA_PREC"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Form the matrix of precession between two epochs (IAU 1976, FK5).
<DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_PREC (EP0, EP1, RMATP)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>EP0</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>beginning epoch</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>EP1</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>ending epoch</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RMATP</EM></TD>
<TH ALIGN="LEFT"><B>D(3,3)</B></TH>
<TD ALIGN="LEFT" NOWRAP>precession matrix</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>The epochs are TDB Julian epochs.
<DT>2.
<DD>The matrix is in the sense:
<BLOCKQUOTE><B>v</B><SUB>1</SUB> = <B>M</B><IMG WIDTH="7" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img72.gif"
ALT="$\cdot$"><B>v</B><SUB>0</SUB></BLOCKQUOTE>
where <B>v</B><SUB>1</SUB> is the star vector relative to the
mean equator and equinox of epoch EP1, <B>M</B> is the
<IMG WIDTH="39" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img18.gif"
ALT="$3\times3$"> matrix RMATP and
<B>v</B><SUB>0</SUB> is the star vector relative to the
mean equator and equinox of epoch EP0.
<DT>3.
<DD>Though the matrix method itself is rigorous, the precession
angles are expressed through canonical polynomials which are
valid only for a limited time span. There are also known
errors in the IAU precession rate. The absolute accuracy
of the present formulation is better than
<IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img25.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$"> from
1960AD to 2040AD, better than <IMG WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img140.gif"
ALT="$1\hspace{-0.05em}^{'\hspace{-0.1em}'}$"> from 1640AD to 2360AD,
and remains below <IMG WIDTH="17" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img75.gif"
ALT="$3\hspace{-0.05em}^{'\hspace{-0.1em}'}$"> for the whole of the period
500BC to 3000AD. The errors exceed <IMG WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img74.gif"
ALT="$10\hspace{-0.05em}^{'\hspace{-0.1em}'}$"> outside the
range 1200BC to 3900AD, exceed <IMG WIDTH="33" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img141.gif"
ALT="$100\hspace{-0.05em}^{'\hspace{-0.1em}'}$"> outside 4200BC to
5600AD and exceed <IMG WIDTH="41" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img142.gif"
ALT="$1000\hspace{-0.05em}^{'\hspace{-0.1em}'}$"> outside 6800BC to 8200AD.
The SLALIB routine sla_PRECL implements a more elaborate
model which is suitable for problems spanning several
thousand years.
</DL></DL>
<P> <DL>
<DT><STRONG>REFERENCES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>Lieske, J.H., 1979. <I>Astr.Astrophys.</I> <B>73</B>, 282;
equations 6 & 7, p283.
<DT>2.
<DD>Kaplan, G.H., 1981. <I>USNO circular no. 163</I>, pA2.
</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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