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<TITLE>SLA_PV2UE - Position/Velocity to Universal Elements</TITLE>
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<H2><A NAME="SECTION0004144000000000000000">SLA_PV2UE - Position/Velocity to Universal Elements</A>
<A NAME="xref_SLA_PV2UE"> </A><A NAME="SLA_PV2UE"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Construct a universal element set based on an instantaneous
position and velocity.
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_PV2UE (PV, DATE, PMASS, U, 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>
</TABLE></DL>
<P> <DL>
<DT><STRONG>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 (Note 3)</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"><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 = too close to Sun</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> -3 = too slow</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>The PV 6-vector can be with respect to any chosen inertial frame,
and the resulting universal-element set will be with respect to
the same frame. A common choice will be mean equator and ecliptic
of epoch J2000.
<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>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.
</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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