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<H2><A NAME="SECTION0004133000000000000000">SLA_PLANEL - Planet Position from Elements</A>
<A NAME="xref_SLA_PLANEL"> </A><A NAME="SLA_PLANEL"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Heliocentric position and velocity of a planet,
asteroid or comet, starting from orbital elements.
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_PLANEL (
DATE, JFORM, EPOCH, ORBINC, ANODE, PERIH,
AORQ, E, AORL, DM, PV, JSTAT)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DATE</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>Modified Julian Date (JD-2400000.5)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>JFORM</EM></TD>
<TD ALIGN="LEFT"><B>I</B></TD>
<TD ALIGN="LEFT" NOWRAP>choice of element set (1-3, see Note 3, below)</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>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</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)</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 JFORM</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> -2 = illegal E</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> -3 = illegal AORQ</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> -4 = illegal DM</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> -5 = numerical error</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>DATE is the instant for which the prediction is
required. It is in the TT timescale (formerly
Ephemeris Time, ET) and is a
Modified Julian Date (JD-2400000.5).
<DT>2.
<DD>The elements are with respect to
the J2000 ecliptic and equinox.
<DT>3.
<DD>Three different element-format options are available, 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>Unused elements (DM for JFORM=2, AORL and DM for JFORM=3) are
not accessed.
<DT>5.
<DD>The reference frame for the result is equatorial and is with
respect to the mean equinox and ecliptic of epoch J2000.
<DT>6.
<DD>The algorithm was originally adapted from the EPHSLA program of
D.H.P.Jones (private communication, 1996). The method
is based on Stumpff's Universal Variables.
</DL></DL>
<P> <DL>
<DT><STRONG>REFERENCE:</STRONG>
<DD>Everhart, E. & Pitkin, E.T., Am. J. Phys. 51, 712, 1983.
</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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