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<H2><A NAME="SECTION000493000000000000000">SLA_FK524 - FK5 to FK4</A>
<A NAME="xref_SLA_FK524"> </A><A NAME="SLA_FK524"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Convert J2000.0 FK5 star data to B1950.0 FK4.
This routine converts stars from the new, IAU 1976, FK5, Fricke
system, to the old, Bessel-Newcomb, FK4 system.
The precepts of Smith <I>et al.</I> (reference 1) are followed,
using the implementation by Yallop <I>et al.</I> (reference 2)
of a matrix method due to Standish. Kinoshita's development of
Andoyer's post-Newcomb precession is used. The numerical
constants from Seidelmann <I>et al.</I> (reference 3) are
used canonically.
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_FK524 (
R2000,D2000,DR2000,DD2000,P2000,V2000,
R1950,D1950,DR1950,DD1950,P1950,V1950)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>R2000</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>J2000.0 <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img24.gif"
ALT="$\alpha$"> (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>D2000</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>J2000.0 <IMG WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img23.gif"
ALT="$\delta$"> (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DR2000</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>J2000.0 proper motion in <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img24.gif"
ALT="$\alpha$">(radians per Julian year)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DD2000</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>J2000.0 proper motion in <IMG WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img23.gif"
ALT="$\delta$">(radians per Julian year)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>P2000</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>J2000.0 parallax (arcsec)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>V2000</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>J2000 radial velocity (km s<SUP>-1</SUP>, +ve = moving away)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>R1950</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>B1950.0 <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img24.gif"
ALT="$\alpha$"> (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>D1950</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>B1950.0 <IMG WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img23.gif"
ALT="$\delta$"> (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DR1950</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>B1950.0 proper motion in <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img24.gif"
ALT="$\alpha$">(radians per tropical year)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DD1950</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>B1950.0 proper motion in <IMG WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img23.gif"
ALT="$\delta$">(radians per tropical year)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>P1950</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>B1950.0 parallax (arcsec)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>V1950</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>radial velocity (km s<SUP>-1</SUP>, +ve = moving away)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>The <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img24.gif"
ALT="$\alpha$"> proper motions are <IMG WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img115.gif"
ALT="$\dot{\alpha}$"> rather than
<IMG WIDTH="48" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img116.gif"
ALT="$\dot{\alpha}\cos\delta$">, and are per year rather than per century.
<DT>2.
<DD>Note that conversion from Julian epoch 2000.0 to Besselian
epoch 1950.0 only is provided for. Conversions involving
other epochs will require use of the appropriate precession,
proper motion, and E-terms routines before and/or after
FK524 is called.
<DT>3.
<DD>In the FK4 catalogue the proper motions of stars within
<IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img117.gif"
ALT="$10^{\circ}$"> of the poles do not include the <I>differential
E-terms</I> effect and should, strictly speaking, be handled
in a different manner from stars outside these regions.
However, given the general lack of homogeneity of the star
data available for routine astrometry, the difficulties of
handling positions that may have been determined from
astrometric fields spanning the polar and non-polar regions,
the likelihood that the differential E-terms effect was not
taken into account when allowing for proper motion in past
astrometry, and the undesirability of a discontinuity in
the algorithm, the decision has been made in this routine to
include the effect of differential E-terms on the proper
motions for all stars, whether polar or not. At epoch 2000,
and measuring on the sky rather than in terms of <IMG WIDTH="27" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img118.gif"
ALT="$\Delta\alpha$">, the errors resulting from this simplification are less than
1 milliarcsecond in position and 1 milliarcsecond per
century in proper motion.
<DT>4.
<DD>See also sla_FK425, sla_FK45Z, sla_FK54Z.
</DL></DL>
<P> <DL>
<DT><STRONG>REFERENCES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>Smith, C.A. <I>et al.</I>, 1989. <I>Astr.J.</I> <B>97</B>, 265.
<DT>2.
<DD>Yallop, B.D. <I>et al.</I>, 1989. <I>Astr.J.</I> <B>97</B>, 274.
<DT>3.
<DD>Seidelmann, P.K. (ed), 1992. <I>Explanatory
Supplement to the Astronomical Almanac,</I> ISBN 0-935702-68-7.
</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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