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| author | Joseph Hunkeler <jhunkeler@gmail.com> | 2015-03-04 21:21:30 -0500 |
|---|---|---|
| committer | Joseph Hunkeler <jhunkeler@gmail.com> | 2015-03-04 21:21:30 -0500 |
| commit | d54fe7c1f704a63824c5bfa0ece65245572e9b27 (patch) | |
| tree | afc52015ffc2c74e0266653eecef1c8ef8ba5d91 /src/slalib/sun67.htx/node156.html | |
| download | calfuse-d54fe7c1f704a63824c5bfa0ece65245572e9b27.tar.gz | |
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diff --git a/src/slalib/sun67.htx/node156.html b/src/slalib/sun67.htx/node156.html new file mode 100644 index 0000000..ab897bc --- /dev/null +++ b/src/slalib/sun67.htx/node156.html @@ -0,0 +1,323 @@ +<!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_PV2EL - Orbital Elements from Position/Velocity</TITLE> +<META NAME="description" CONTENT="SLA_PV2EL - Orbital Elements from Position/Velocity"> +<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="node157.html"> +<LINK REL="previous" HREF="node155.html"> +<LINK REL="up" HREF="node13.html"> +<LINK REL="next" HREF="node157.html"> +</HEAD> +<BODY > +<BR> <HR> +<A NAME="tex2html1986" HREF="node157.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html1984" HREF="node13.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html1978" HREF="node155.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="tex2html1987" HREF="node157.html">SLA_PV2UE - Position/Velocity to Universal Elements</A> +<BR> +<B>Up:</B> <A NAME="tex2html1985" HREF="node13.html">SUBPROGRAM SPECIFICATIONS</A> +<BR> +<B> Previous:</B> <A NAME="tex2html1979" HREF="node155.html">SLA_PRENUT - Precession/Nutation Matrix</A> +<BR> <HR> <P> +<P><!--End of Navigation Panel--> +<H2><A NAME="SECTION0004143000000000000000">SLA_PV2EL - Orbital Elements from Position/Velocity</A> +<A NAME="xref_SLA_PV2EL"> </A><A NAME="SLA_PV2EL"> </A> +</H2> + <DL> +<DT><STRONG>ACTION:</STRONG> +<DD>Heliocentric osculating elements obtained from instantaneous +position and velocity. +<P> <DT><STRONG>CALL:</STRONG> +<DD><TT>CALL sla_PV2EL ( + PV, DATE, PMASS, 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>PV</EM></TD> +<TH ALIGN="LEFT"><B>D(6)</B></TH> +<TD ALIGN="LEFT" NOWRAP>heliocentric <IMG WIDTH="106" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" + SRC="img51.gif" + ALT="$[\,x,y,z,\dot{x},\dot{y},\dot{z}\,]$">, equatorial, J2000</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD> +<TD ALIGN="LEFT"><B></B></TD> +<TD ALIGN="LEFT" NOWRAP> (AU, AU/s; Note 1)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DATE</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP>date (TT Modified Julian Date = JD-2400000.5)</TD> +</TR> +<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PMASS</EM></TD> +<TD ALIGN="LEFT"><B>D</B></TD> +<TD ALIGN="LEFT" NOWRAP>mass of the planet (Sun = 1; Note 2)</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 PV 6-vector is 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>2. +<DD>The mass, PMASS, is important only for the larger planets. For + most purposes (<I>e.g.</I> asteroids) use 0D0. Values less than zero + are illegal. + <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>REFERENCE:</STRONG> +<DD>Sterne, Theodore E., <I>An Introduction to Celestial Mechanics,</I> +Interscience Publishers, 1960. + </DL> +<BR> <HR> +<A NAME="tex2html1986" HREF="node157.html"> +<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A> +<A NAME="tex2html1984" HREF="node13.html"> +<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A> +<A NAME="tex2html1978" HREF="node155.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="tex2html1987" HREF="node157.html">SLA_PV2UE - Position/Velocity to Universal Elements</A> +<BR> +<B>Up:</B> <A NAME="tex2html1985" HREF="node13.html">SUBPROGRAM SPECIFICATIONS</A> +<BR> +<B> Previous:</B> <A NAME="tex2html1979" HREF="node155.html">SLA_PRENUT - Precession/Nutation Matrix</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> |