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- Transform conventional elements into position and velocity
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<H2><A NAME="SECTION000449000000000000000"></A><A NAME="____palPlanel_"></A>
<BR>
palPlanel

   palPlanel
-   Transform conventional elements into position and velocity

</H2>
      <DL>
<DT><STRONG>Description:</STRONG></DT>
<DD><DL>
<DD>Heliocentric position and velocity of a planet, asteroid or comet,
      starting from orbital elements.

</DD>
</DL>
      
<BR>   
   
</DD>
<DT><STRONG>Invocation:</STRONG></DT>
<DD><DL>
<DD><TT>      void palPlanel ( double date, int jform, double epoch, double orbinc,
                       double anode, double perih, double aorq, double e,
                       double aorl, double dm, double pv[6], int <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$*$"></SPAN>jstat );
   </TT>
      
</DD>
</DL>
      
<BR>

</DD>
<DT><STRONG>Arguments:</STRONG></DT>
<DD>
<BR>      <DL>
<DT><STRONG>
         date = double (Given)
      </STRONG></DT>
<DD>
         Epoch (TT MJD) of osculation (Note 1)
      
      
</DD>
<DT><STRONG>
         jform = int (Given)
      </STRONG></DT>
<DD>
         Element set actually returned (1-3; Note 3)
      
      
</DD>
<DT><STRONG>
         epoch = double (Given)
      </STRONG></DT>
<DD>
         Epoch of elements (TT MJD) (Note 4)
      
      
</DD>
<DT><STRONG>
         orbinc = double (Given)
      </STRONG></DT>
<DD>
         inclination (radians)
      
      
</DD>
<DT><STRONG>
         anode = double (Given)
      </STRONG></DT>
<DD>
         longitude of the ascending node (radians)
      
      
</DD>
<DT><STRONG>
         perih = double (Given)
      </STRONG></DT>
<DD>
         longitude or argument of perihelion (radians)
      
      
</DD>
<DT><STRONG>
         aorq = double (Given)
      </STRONG></DT>
<DD>
         mean distance or perihelion distance (AU)
      
      
</DD>
<DT><STRONG>
         e = double (Given)
      </STRONG></DT>
<DD>
         eccentricity
      
      
</DD>
<DT><STRONG>
         aorl = double (Given)
      </STRONG></DT>
<DD>
         mean anomaly or longitude (radians, JFORM=1,2 only)
      
      
</DD>
<DT><STRONG>
         dm = double (Given)
      </STRONG></DT>
<DD>
         daily motion (radians, JFORM=1 only)
      
      
</DD>
<DT><STRONG>
         u = double [13] (Returned)
      </STRONG></DT>
<DD>
         Universal orbital elements (Note 1)
             (0)  combined mass (M<SPAN CLASS="MATH"><IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.png"
 ALT="$+$"></SPAN>m)
             (1)  total energy of the orbit (alpha)
             (2)  reference (osculating) epoch (t0)
           (3-5)  position at reference epoch (r0)
           (6-8)  velocity at reference epoch (v0)
             (9)  heliocentric distance at reference epoch
            (10)  r0.v0
            (11)  date (t)
            (12)  universal eccentric anomaly (psi) of date, approx
      
      
</DD>
<DT><STRONG>
         jstat = int <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$*$"></SPAN> (Returned)
      </STRONG></DT>
<DD>
         status:  0 = OK

<UL>
<LI>-1 = illegal JFORM

<P>
</LI>
<LI>-2 = illegal E

<P>
</LI>
<LI>-3 = illegal AORQ

<P>
</LI>
<LI>-4 = illegal DM

<P>
</LI>
<LI>-5 = numerical error

</LI>
</UL>
      
<BR>   
      

</DD>
</DL>
      
<BR>   
   
</DD>
<DT><STRONG>Notes:</STRONG></DT>
<DD><UL>
<LI>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).

<P>
</LI>
<LI>The elements are with respect to the J2000 ecliptic and equinox.

<P>
</LI>
<LI>A choice of three different element-set options is available:

<P>
</LI>
</UL>
      
<BR>
Option JFORM = 1, suitable for the major planets:

<P>
EPOCH  = epoch of elements (TT MJD)
          ORBINC = inclination i (radians)
          ANODE  = longitude of the ascending node, big omega (radians)
          PERIH  = longitude of perihelion, curly pi (radians)
          AORQ   = mean distance, a (AU)
          E      = eccentricity, e (range 0 to <SPAN CLASS="MATH"><IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.png"
 ALT="$&lt;$"></SPAN>1)
          AORL   = mean longitude L (radians)
          DM     = daily motion (radians)

<P>
Option JFORM = 2, suitable for minor planets:

<P>
EPOCH  = epoch of elements (TT MJD)
          ORBINC = inclination i (radians)
          ANODE  = longitude of the ascending node, big omega (radians)
          PERIH  = argument of perihelion, little omega (radians)
          AORQ   = mean distance, a (AU)
          E      = eccentricity, e (range 0 to <SPAN CLASS="MATH"><IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.png"
 ALT="$&lt;$"></SPAN>1)
          AORL   = mean anomaly M (radians)

<P>
Option JFORM = 3, suitable for comets:

<P>
EPOCH  = epoch of elements and perihelion (TT MJD)
          ORBINC = inclination i (radians)
          ANODE  = longitude of the ascending node, big omega (radians)
          PERIH  = argument of perihelion, little omega (radians)
          AORQ   = perihelion distance, q (AU)
          E      = eccentricity, e (range 0 to 10)

<P>
Unused arguments (DM for JFORM=2, AORL and DM for JFORM=3) are not
        accessed.

<UL>
<LI>Each of the three element sets defines an unperturbed heliocentric
           orbit.  For a given epoch of observation, the position of the body
           in its orbit can be predicted from these elements, which are
           called <TT>"</TT>osculating elements<TT>"</TT>, using standard two-body analytical
           solutions.  However, due to planetary perturbations, a given set
           of osculating elements remains usable for only as long as the
           unperturbed orbit that it describes is an adequate approximation
           to reality.  Attached to such a set of elements is a date called
           the <TT>"</TT>osculating epoch<TT>"</TT>, at which the elements are, momentarily,
           a perfect representation of the instantaneous position and
           velocity of the body.

<P>
</LI>
</UL>
      
<BR>
Therefore, for any given problem there are up to three different
        epochs in play, and it is vital to distinguish clearly between
        them:

<P>
. The epoch of observation:  the moment in time for which the
          position of the body is to be predicted.

<P>
. The epoch defining the position of the body:  the moment in time
          at which, in the absence of purturbations, the specified
          position (mean longitude, mean anomaly, or perihelion) is
          reached.

<P>
. The osculating epoch:  the moment in time at which the given
          elements are correct.

<P>
For the major-planet and minor-planet cases it is usual to make
        the epoch that defines the position of the body the same as the
        epoch of osculation.  Thus, only two different epochs are
        involved:  the epoch of the elements and the epoch of observation.

<P>
For comets, the epoch of perihelion fixes the position in the
        orbit and in general a different epoch of osculation will be
        chosen.  Thus, all three types of epoch are involved.

<P>
For the present routine:

<P>
. The epoch of observation is the argument DATE.

<P>
. The epoch defining the position of the body is the argument
          EPOCH.

<P>
. The osculating epoch is not used and is assumed to be close
          enough to the epoch of observation to deliver adequate accuracy.
          If not, a preliminary call to sla_PERTEL may be used to update
          the element-set (and its associated osculating epoch) by
          applying planetary perturbations.

<UL>
<LI>The reference frame for the result is with respect to the mean
           equator and equinox of epoch J2000.

<P>
</LI>
<LI>The algorithm was originally adapted from the EPHSLA program of
           D.H.P.Jones (private communication, 1996).  The method is based
           on Stumpff<TT>'</TT>s Universal Variables.

</LI>
</UL>
      
<BR>

</DD>
<DT><STRONG>
      See Also
   </STRONG></DT>
<DD>Everhart, E. &amp; Pitkin, E.T., Am.J.Phys. 51, 712, 1983.

</DD>
</DL>
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