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diff --git a/src/slalib/sun67.htx/node169.html b/src/slalib/sun67.htx/node169.html new file mode 100644 index 0000000..6180ab0 --- /dev/null +++ b/src/slalib/sun67.htx/node169.html @@ -0,0 +1,275 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"> +<!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997) + by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds +* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan +* with significant contributions from: + Jens Lippman, Marek Rouchal, Martin Wilck and others --> +<HTML> +<HEAD> +<TITLE>SLA_REFZ - Apply Refraction to ZD</TITLE> +<META NAME="description" CONTENT="SLA_REFZ - Apply Refraction to ZD"> +<META NAME="keywords" CONTENT="sun67"> +<META NAME="resource-type" CONTENT="document"> +<META NAME="distribution" CONTENT="global"> +<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso_8859_1"> +<LINK REL="STYLESHEET" HREF="sun67.css"> +<LINK REL="next" HREF="node170.html"> +<LINK REL="previous" HREF="node168.html"> +<LINK REL="up" HREF="node13.html"> +<LINK REL="next" HREF="node170.html"> +</HEAD> +<BODY > +<BR> <HR> +<A NAME="tex2html2116" HREF="node170.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2114" HREF="node13.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2108" HREF="node168.html"> +<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0" + SRC="contents_motif.gif"></A> +<BR> +<B> Next:</B> <A NAME="tex2html2117" HREF="node170.html">SLA_RVEROT - RV Corrn to Earth Centre</A> +<BR> +<B>Up:</B> <A NAME="tex2html2115" HREF="node13.html">SUBPROGRAM SPECIFICATIONS</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2109" HREF="node168.html">SLA_REFV - Apply Refraction to Vector</A> +<BR> <HR> <P> +<P><!--End of Navigation Panel--> +<H2><A NAME="SECTION0004156000000000000000">SLA_REFZ - Apply Refraction to ZD</A> +<A NAME="xref_SLA_REFZ"> </A><A NAME="SLA_REFZ"> </A> +</H2> + <DL> +<DT><STRONG>ACTION:</STRONG> +<DD>Adjust an unrefracted zenith distance to include the effect of +atmospheric refraction, using the simple + <IMG WIDTH="164" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" + SRC="img148.gif" + ALT="$\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$"> model. +<P> <DT><STRONG>CALL:</STRONG> +<DD><TT>CALL sla_REFZ (ZU, REFA, REFB, ZR)</TT> +<P> </DL> +<P> <DL> +<DT><STRONG>GIVEN:</STRONG> +<DD> +<BR> +<TABLE CELLPADDING=3> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ZU</EM></TD> +<TH ALIGN="LEFT"><B>D</B></TH> +<TD ALIGN="LEFT" NOWRAP>unrefracted zenith distance of the source (radians)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>REFA</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP><IMG WIDTH="37" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img151.gif" + ALT="$\tan \zeta$"> coefficient (radians)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>REFB</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP><IMG WIDTH="44" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" + SRC="img152.gif" + ALT="$\tan^{3} \zeta$"> coefficient (radians)</TD> +</TR> +</TABLE></DL> +<P> <DL> +<DT><STRONG>RETURNED:</STRONG> +<DD> +<BR> +<TABLE CELLPADDING=3> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ZR</EM></TD> +<TH ALIGN="LEFT"><B>D</B></TH> +<TD ALIGN="LEFT" NOWRAP>refracted zenith distance (radians)</TD> +</TR> +</TABLE></DL> +<P> <DL> +<DT><STRONG>NOTES:</STRONG> +<DD><DL COMPACT> +<DT>1. +<DD>This routine applies the adjustment for refraction in the +opposite sense to the usual one - it takes an unrefracted +(<I>in vacuo</I>) position and produces an observed (refracted) + position, whereas the + <IMG WIDTH="164" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" + SRC="img148.gif" + ALT="$\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$"> model strictly + applies to the case where an observed position is to have the + refraction removed. The unrefracted to refracted case is + harder, and requires an inverted form of the text-book + refraction models; the formula used here is based on the + Newton-Raphson method. For the utmost numerical consistency + with the refracted to unrefracted model, two iterations are + carried out, achieving agreement at the 10<SUP>-11</SUP> arcsecond level + for <IMG WIDTH="56" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img208.gif" + ALT="$\zeta=80^\circ$">. The inherent accuracy of the model + is, of course, far worse than this - see the documentation for + sla_REFCO for more information. + <DT>2. +<DD>At <IMG WIDTH="56" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img209.gif" + ALT="$\zeta=83^\circ$">, the rapidly-worsening + <IMG WIDTH="164" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" + SRC="img148.gif" + ALT="$\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$"> model is abandoned and an empirical formula takes over: +<P> +<P ALIGN="CENTER"><IMG WIDTH="321" HEIGHT="49" + SRC="img210.gif" + ALT="\begin{displaymath} +\Delta \zeta = F \left( + \frac{0^\circ\hspace{-0.37em}.\hspa... + ...hspace{0.02em}00202 E^2} + {1 + 0.28385 E +0.02390 E^2} \right) \end{displaymath}"></P> +where <IMG WIDTH="113" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img211.gif" + ALT="$E=90^\circ-\zeta_{true}$"> and <I>F</I> is a factor chosen to meet the + <IMG WIDTH="164" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" + SRC="img148.gif" + ALT="$\Delta \zeta = a \tan \zeta + b \tan^{3} \zeta$"> formula at <IMG WIDTH="56" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img209.gif" + ALT="$\zeta=83^\circ$">. Over a + wide range of observer heights and corresponding temperatures and + pressures, the following levels of accuracy are achieved, + relative to numerical integration through a model atmosphere: +<P> <DIV ALIGN="CENTER"> +<TABLE CELLPADDING=3> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="28" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img184.gif" + ALT="$\zeta_{obs}$"></TD> +<TH ALIGN="CENTER" NOWRAP><I>error</I></TH> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP> </TD> +<TD ALIGN="CENTER" NOWRAP> </TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img179.gif" + ALT="$80^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img185.gif" + ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.4$"></TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img186.gif" + ALT="$81^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img187.gif" + ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$"></TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img188.gif" + ALT="$82^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img212.gif" + ALT="$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$"></TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img190.gif" + ALT="$83^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img213.gif" + ALT="$3\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$"></TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img191.gif" + ALT="$84^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img214.gif" + ALT="$4\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.9$"></TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img193.gif" + ALT="$85^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img215.gif" + ALT="$5\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$"></TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img194.gif" + ALT="$86^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img216.gif" + ALT="$6\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$"></TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img196.gif" + ALT="$87^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img217.gif" + ALT="$7\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$"></TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img198.gif" + ALT="$88^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0" + SRC="img43.gif" + ALT="$11\hspace{-0.05em}^{'\hspace{-0.1em}'}$"></TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img200.gif" + ALT="$89^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0" + SRC="img218.gif" + ALT="$21\hspace{-0.05em}^{'\hspace{-0.1em}'}$"></TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img22.gif" + ALT="$90^{\circ}$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img219.gif" + ALT="$43\hspace{-0.05em}^{'\hspace{-0.1em}'}$"></TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img203.gif" + ALT="$91^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img220.gif" + ALT="$92\hspace{-0.05em}^{'\hspace{-0.1em}'}$"></TD> +<TD ALIGN="LEFT" NOWRAP>< high-altitude</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP><IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img205.gif" + ALT="$92^\circ$"></TD> +<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="33" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" + SRC="img221.gif" + ALT="$220\hspace{-0.05em}^{'\hspace{-0.1em}'}$"></TD> +<TD ALIGN="LEFT" NOWRAP>< sites only</TD> +</TR> +</TABLE></DIV> + <DT>3. +<DD>See also the routine sla_REFV, which performs the adjustment in + <IMG WIDTH="58" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img50.gif" + ALT="$[\,x,y,z\,]$">, and with the emphasis on speed rather than numerical accuracy. + </DL></DL> +<BR> <HR> +<A NAME="tex2html2116" HREF="node170.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2114" HREF="node13.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2108" HREF="node168.html"> +<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0" + SRC="contents_motif.gif"></A> +<BR> +<B> Next:</B> <A NAME="tex2html2117" HREF="node170.html">SLA_RVEROT - RV Corrn to Earth Centre</A> +<BR> +<B>Up:</B> <A NAME="tex2html2115" HREF="node13.html">SUBPROGRAM SPECIFICATIONS</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2109" HREF="node168.html">SLA_REFV - Apply Refraction to Vector</A> +<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> +</BODY> +</HTML> |