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<H2><A NAME="SECTION0004175000000000000000">SLA_UE2PV - Pos/Vel from Universal Elements</A>
<A NAME="xref_SLA_UE2PV"> </A><A NAME="SLA_UE2PV"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Heliocentric position and velocity of a planet, asteroid or comet,
starting from orbital elements in the ``universal variables'' form.
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_UE2PV (DATE, U, 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>date (TT Modified Julian Date = JD-2400000.5)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>GIVEN and RETURNED:</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>
</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; Note 1)</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 = radius vector zero</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> -2 = failed to converge</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).
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 companion routine is sla_EL2UE. This takes the conventional
orbital elements and transforms them into the set of numbers
needed by the present routine. A single prediction requires one
one call to sla_EL2UE followed by one call to the present routine;
for convenience, the two calls are packaged as the routine
sla_PLANEL. Multiple predictions may be made by again
calling sla_EL2UE once, but then calling the present routine
multiple times, which is faster than multiple calls to sla_PLANEL.
<P>
It is not obligatory to use sla_EL2UE to obtain the parameters.
However, it should be noted that because sla_EL2UE performs its
own validation, no checks on the contents of the array U are made
by the present routine.
<DT>3.
<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>4.
<DD>The universal elements supplied in the array U are in canonical
units (solar masses, AU and canonical days). The position and
velocity are not sensitive to the choice of reference frame. The
sla_EL2UE routine in fact produces coordinates with respect to the
J2000 equator and equinox.
<DT>5.
<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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