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diff --git a/src/slalib/sun67.htx/node187.html b/src/slalib/sun67.htx/node187.html new file mode 100644 index 0000000..9b71eb3 --- /dev/null +++ b/src/slalib/sun67.htx/node187.html @@ -0,0 +1,378 @@ +<!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_UE2EL - Universal to Conventional Elements</TITLE> +<META NAME="description" CONTENT="SLA_UE2EL - Universal to Conventional Elements"> +<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="node188.html"> +<LINK REL="previous" HREF="node186.html"> +<LINK REL="up" HREF="node13.html"> +<LINK REL="next" HREF="node188.html"> +</HEAD> +<BODY > +<BR> <HR> +<A NAME="tex2html2296" HREF="node188.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2294" HREF="node13.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2288" HREF="node186.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="tex2html2297" HREF="node188.html">SLA_UE2PV - Pos/Vel from Universal Elements</A> +<BR> +<B>Up:</B> <A NAME="tex2html2295" HREF="node13.html">SUBPROGRAM SPECIFICATIONS</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2289" HREF="node186.html">SLA_TPV2C - Plate centre from and x,y,z</A> +<BR> <HR> <P> +<P><!--End of Navigation Panel--> +<H2><A NAME="SECTION0004174000000000000000">SLA_UE2EL - Universal to Conventional Elements</A> +<A NAME="xref_SLA_UE2EL"> </A><A NAME="SLA_UE2EL"> </A> +</H2> + <DL> +<DT><STRONG>ACTION:</STRONG> +<DD>Transform universal elements into conventional heliocentric +osculating elements. +<P> <DT><STRONG>CALL:</STRONG> +<DD><TT>CALL sla_UE2EL ( + U, JFORMR, + JFORM, EPOCH, ORBINC, ANODE, PERIH, + AORQ, E, AORL, DM, JSTAT)</TT> +<P> </DL> +<P> <DL> +<DT><STRONG>GIVEN:</STRONG> +<DD> +<BR> +<TABLE CELLPADDING=3> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>U</EM></TD> +<TH ALIGN="LEFT"><B>D(13)</B></TH> +<TD ALIGN="LEFT" NOWRAP>universal orbital elements (updated; Note 1)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(1)</TD> +<TD></TD> +<TD ALIGN="LEFT" NOWRAP>combined mass (<I>M</I>+<I>m</I>)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(2)</TD> +<TD></TD> +<TD ALIGN="LEFT" NOWRAP>total energy of the orbit (<IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img24.gif" + ALT="$\alpha$">)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(3)</TD> +<TD></TD> +<TD ALIGN="LEFT" NOWRAP>reference (osculating) epoch (<I>t<SUB>0</SUB></I>)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(4-6)</TD> +<TD></TD> +<TD ALIGN="LEFT" NOWRAP>position at reference epoch (<IMG WIDTH="17" HEIGHT="25" ALIGN="MIDDLE" BORDER="0" + SRC="img102.gif" + ALT="${\rm \bf r}_0$">)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(7-9)</TD> +<TD></TD> +<TD ALIGN="LEFT" NOWRAP>velocity at reference epoch (<IMG WIDTH="19" HEIGHT="25" ALIGN="MIDDLE" BORDER="0" + SRC="img103.gif" + ALT="${\rm \bf v}_0$">)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(10)</TD> +<TD></TD> +<TD ALIGN="LEFT" NOWRAP>heliocentric distance at reference epoch</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(11)</TD> +<TD></TD> +<TD ALIGN="LEFT" NOWRAP><IMG WIDTH="39" HEIGHT="25" ALIGN="MIDDLE" BORDER="0" + SRC="img104.gif" + ALT="${\rm \bf r}_0.{\rm \bf v}_0$"></TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(12)</TD> +<TD></TD> +<TD ALIGN="LEFT" NOWRAP>date (<I>t</I>)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="CENTER" NOWRAP COLSPAN=1>(13)</TD> +<TD></TD> +<TD ALIGN="LEFT" NOWRAP>universal eccentric anomaly (<IMG WIDTH="14" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img105.gif" + ALT="$\psi$">) of date, approx</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"> </TD> +<TD ALIGN="LEFT"> </TD> +<TD ALIGN="LEFT" NOWRAP> </TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>JFORMR</EM></TD> +<TD ALIGN="LEFT"><B>I</B></TD> +<TD ALIGN="LEFT" NOWRAP>requested element set (1-3; Note 3)</TD> +</TR> +</TABLE></DL> +<P> <DL> +<DT><STRONG>RETURNED:</STRONG> +<DD> +<BR> +<TABLE CELLPADDING=3> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>JFORM</EM></TD> +<TH ALIGN="LEFT"><B>I</B></TH> +<TD ALIGN="LEFT" NOWRAP>element set actually returned (1-3; Note 4)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>EPOCH</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP>epoch of elements (<I>t<SUB>0</SUB></I> or <I>T</I>, TT MJD)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ORBINC</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP>inclination (<I>i</I>, radians)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ANODE</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP>longitude of the ascending node (<IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$">, radians)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PERIH</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP>longitude or argument of perihelion +(<IMG WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img100.gif" + ALT="$\varpi$"> or <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img101.gif" + ALT="$\omega$">,</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD> +<TD ALIGN="LEFT"><B></B></TD> +<TD ALIGN="LEFT" NOWRAP> radians)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>AORQ</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP>mean distance or perihelion distance (<I>a</I> or <I>q</I>, AU)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>E</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP>eccentricity (<I>e</I>)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>AORL</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP>mean anomaly or longitude +(<I>M</I> or <I>L</I>, radians,</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD> +<TD ALIGN="LEFT"><B></B></TD> +<TD ALIGN="LEFT" NOWRAP> JFORM=1,2 only)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DM</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP>daily motion (<I>n</I>, radians, JFORM=1 only)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>JSTAT</EM></TD> +<TD ALIGN="LEFT"><B>I</B></TD> +<TD ALIGN="LEFT" NOWRAP>status:</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD> +<TD ALIGN="LEFT"><B></B></TD> +<TD ALIGN="LEFT" NOWRAP> 0 = OK</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD> +<TD ALIGN="LEFT"><B></B></TD> +<TD ALIGN="LEFT" NOWRAP> -1 = illegal PMASS</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD> +<TD ALIGN="LEFT"><B></B></TD> +<TD ALIGN="LEFT" NOWRAP> -2 = illegal JFORMR</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD> +<TD ALIGN="LEFT"><B></B></TD> +<TD ALIGN="LEFT" NOWRAP> -3 = position/velocity out of allowed range</TD> +</TR> +</TABLE></DL> +<P> <DL> +<DT><STRONG>NOTES:</STRONG> +<DD><DL COMPACT> +<DT>1. +<DD>The ``universal'' elements are those which define the orbit for the +purposes of the method of universal variables (see reference 2). +They consist of the combined mass of the two bodies, an epoch, + and the position and velocity vectors (arbitrary reference frame) + at that epoch. The parameter set used here includes also various + quantities that can, in fact, be derived from the other + information. This approach is taken to avoiding unnecessary + computation and loss of accuracy. The supplementary quantities + are (i) <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img24.gif" + ALT="$\alpha$">, which is proportional to the total energy of the + orbit, (ii) the heliocentric distance at epoch, + (iii) the outwards component of the velocity at the given epoch, + (iv) an estimate of <IMG WIDTH="14" HEIGHT="27" ALIGN="MIDDLE" BORDER="0" + SRC="img105.gif" + ALT="$\psi$">, the ``universal eccentric anomaly'' at a + given date and (v) that date. + <DT>2. +<DD>The universal elements are with respect to the mean equator and + equinox of epoch J2000. The orbital elements produced are with + respect to the J2000 ecliptic and mean equinox. + <DT>3. +<DD>Three different element-format options are supported, as + follows. <BR> +<P> +JFORM=1, suitable for the major planets: +<P> <PRE><TT> + EPOCH = epoch of elements <I>t<SUB>0</SUB></I> (TT MJD) + ORBINC = inclination <I>i</I> (radians) + ANODE = longitude of the ascending node <IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$"> (radians) + PERIH = longitude of perihelion <IMG WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img100.gif" + ALT="$\varpi$"> (radians) + AORQ = mean distance <I>a</I> (AU) + E = eccentricity <I>e</I> <IMG WIDTH="83" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img106.gif" + ALT="$( 0 \leq e < 1 )$"> + AORL = mean longitude <I>L</I> (radians) + DM = daily motion <I>n</I> (radians) +</TT></PRE> +<P> +JFORM=2, suitable for minor planets: +<P> <PRE><TT> + EPOCH = epoch of elements <I>t<SUB>0</SUB></I> (TT MJD) + ORBINC = inclination <I>i</I> (radians) + ANODE = longitude of the ascending node <IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$"> (radians) + PERIH = argument of perihelion <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img101.gif" + ALT="$\omega$"> (radians) + AORQ = mean distance <I>a</I> (AU) + E = eccentricity <I>e</I> <IMG WIDTH="83" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img106.gif" + ALT="$( 0 \leq e < 1 )$"> + AORL = mean anomaly <I>M</I> (radians) +</TT></PRE> +<P> +JFORM=3, suitable for comets: +<P> <PRE><TT> + EPOCH = epoch of perihelion <I>T</I> (TT MJD) + ORBINC = inclination <I>i</I> (radians) + ANODE = longitude of the ascending node <IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$"> (radians) + PERIH = argument of perihelion <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img101.gif" + ALT="$\omega$"> (radians) + AORQ = perihelion distance <I>q</I> (AU) + E = eccentricity <I>e</I> <IMG WIDTH="91" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img107.gif" + ALT="$( 0 \leq e \leq 10 )$"></TT></PRE> + <DT>4. +<DD>It may not be possible to generate elements in the form + requested through JFORMR. The caller is notified of the form + of elements actually returned by means of the JFORM argument: +<P> <PRE><TT> + JFORMR JFORM meaning + + 1 1 OK: elements are in the requested format + 1 2 never happens + 1 3 orbit not elliptical + 2 1 never happens + 2 2 OK: elements are in the requested format + 2 3 orbit not elliptical + 3 1 never happens + 3 2 never happens + 3 3 OK: elements are in the requested format +</TT></PRE> + <DT>5. +<DD>The arguments returned for each value of JFORM (<I>cf</I> Note 5: + JFORM may not be the same as JFORMR) are as follows: +<P> <PRE><TT> + JFORM 1 2 3 + + EPOCH <I>t<SUB>0</SUB></I> <I>t<SUB>0</SUB></I> <I>T</I> + ORBINC <I>i</I> <I>i</I> <I>i</I> + ANODE <IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$"> <IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$"> <IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$"> + PERIH <IMG WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img100.gif" + ALT="$\varpi$"> <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img101.gif" + ALT="$\omega$"> <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img101.gif" + ALT="$\omega$"> + AORQ <I>a</I> <I>a</I> <I>q</I> + E <I>e</I> <I>e</I> <I>e</I> + AORL <I>L</I> <I>M</I> - + DM <I>n</I> - - +</TT></PRE> +<P> +where: + <PRE><TT> + <I>t<SUB>0</SUB></I> is the epoch of the elements (MJD, TT) + <I>T</I> is the epoch of perihelion (MJD, TT) + <I>i</I> is the inclination (radians) + <IMG WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" + SRC="img99.gif" + ALT="$\Omega$"> is the longitude of the ascending node (radians) + <IMG WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img100.gif" + ALT="$\varpi$"> is the longitude of perihelion (radians) + <IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img101.gif" + ALT="$\omega$"> is the argument of perihelion (radians) + <I>a</I> is the mean distance (AU) + <I>q</I> is the perihelion distance (AU) + <I>e</I> is the eccentricity + <I>L</I> is the longitude (radians, <IMG WIDTH="48" HEIGHT="25" ALIGN="MIDDLE" BORDER="0" + SRC="img143.gif" + ALT="$0-2\pi$">) <I>M</I> is the mean anomaly (radians, <IMG WIDTH="48" HEIGHT="25" ALIGN="MIDDLE" BORDER="0" + SRC="img143.gif" + ALT="$0-2\pi$">) <I>n</I> is the daily motion (radians) + - means no value is set +</TT></PRE> + <DT>6. +<DD>At very small inclinations, the longitude of the ascending node + ANODE becomes indeterminate and under some circumstances may be + set arbitrarily to zero. Similarly, if the orbit is close to + circular, the true anomaly becomes indeterminate and under some + circumstances may be set arbitrarily to zero. In such cases, + the other elements are automatically adjusted to compensate, + and so the elements remain a valid description of the orbit. + </DL></DL> +<P> <DL> +<DT><STRONG>REFERENCES:</STRONG> +<DD><DL COMPACT> +<DT>1. +<DD>Sterne, Theodore E., <I>An Introduction to Celestial Mechanics,</I> +Interscience Publishers, 1960. Section 6.7, p199. +<DT>2. +<DD>Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983. + </DL></DL> +<BR> <HR> +<A NAME="tex2html2296" HREF="node188.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html2294" HREF="node13.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html2288" HREF="node186.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="tex2html2297" HREF="node188.html">SLA_UE2PV - Pos/Vel from Universal Elements</A> +<BR> +<B>Up:</B> <A NAME="tex2html2295" HREF="node13.html">SUBPROGRAM SPECIFICATIONS</A> +<BR> +<B> Previous:</B> <A NAME="tex2html2289" HREF="node186.html">SLA_TPV2C - Plate centre from and x,y,z</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> |