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<H2><A NAME="SECTION0004172000000000000000"> </A><A NAME="xref_SLA_TPS2C"> </A><A NAME="SLA_TPS2C"> </A>
<BR>
SLA_TPS2C - Plate centre from <IMG WIDTH="26" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img90.gif"
ALT="$\xi,\eta$"> and <IMG WIDTH="28" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img91.gif"
ALT="$\alpha,\delta$"></H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>From the tangent plane coordinates of a star of known <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$">,determine the <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img3.gif"
ALT="$[\,\alpha,\delta\,]$"> of the tangent point (single precision)
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_TPS2C (XI, ETA, RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2, N)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>XI,ETA</EM></TD>
<TH ALIGN="LEFT"><B>R</B></TH>
<TD ALIGN="LEFT" NOWRAP>tangent plane rectangular coordinates (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RA,DEC</EM></TD>
<TD ALIGN="LEFT"><B>R</B></TD>
<TD ALIGN="LEFT" NOWRAP>spherical coordinates (radians)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RAZ1,DECZ1</EM></TD>
<TH ALIGN="LEFT"><B>R</B></TH>
<TD ALIGN="LEFT" NOWRAP>spherical coordinates of tangent point,
solution 1</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RAZ2,DECZ2</EM></TD>
<TD ALIGN="LEFT"><B>R</B></TD>
<TD ALIGN="LEFT" NOWRAP>spherical coordinates of tangent point,
solution 2</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>N</EM></TD>
<TD ALIGN="LEFT"><B>I</B></TD>
<TD ALIGN="LEFT" NOWRAP>number of solutions:</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> 0 = no solutions returned (note 2)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> 1 = only the first solution is useful (note 3)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> 2 = there are two useful solutions (note 3)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>The RAZ1 and RAZ2 values returned are in the range <IMG WIDTH="43" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img66.gif"
ALT="$0\!-\!2\pi$">.<DT>2.
<DD>Cases where there is no solution can only arise near the poles.
For example, it is clearly impossible for a star at the pole
itself to have a non-zero <IMG WIDTH="10" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img92.gif"
ALT="$\xi$"> value, and hence it is
meaningless to ask where the tangent point would have to be
to bring about this combination of <IMG WIDTH="10" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
SRC="img92.gif"
ALT="$\xi$"> and <IMG WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img23.gif"
ALT="$\delta$">. <DT>3.
<DD>Also near the poles, cases can arise where there are two useful
solutions. The argument N indicates whether the second of the
two solutions returned is useful. N=1
indicates only one useful solution, the usual case; under
these circumstances, the second solution corresponds to the
``over-the-pole'' case, and this is reflected in the values
of RAZ2 and DECZ2 which are returned.
<DT>4.
<DD>The DECZ1 and DECZ2 values returned are in the range <IMG WIDTH="25" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img47.gif"
ALT="$\pm \pi$">, but in the ordinary, non-pole-crossing, case, the range is
<IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img15.gif"
ALT="$\pm\pi/2$">. <DT>5.
<DD>RA, DEC, RAZ1, DECZ1, RAZ2, DECZ2 are all in radians.
<DT>6.
<DD>The projection is called the <I>gnomonic</I> projection; the
Cartesian coordinates <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img85.gif"
ALT="$[\,\xi,\eta\,]$"> are called
<I>standard coordinates.</I> The latter
are in units of the distance from the tangent plane to the projection
point, <I>i.e.</I> radians near the origin.
<DT>7.
<DD>When working in <IMG WIDTH="58" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img50.gif"
ALT="$[\,x,y,z\,]$"> rather than spherical coordinates, the
equivalent Cartesian routine sla_TPV2C is available.
</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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