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- Topocentric RA,Dec of a Solar-System object from heliocentric orbital elements
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<H2><A NAME="SECTION000451000000000000000"></A><A NAME="____palPlante_"></A>
<BR>
palPlante

   palPlante
-   Topocentric RA,Dec of a Solar-System object from heliocentric orbital elements

</H2>
      <DL>
<DT><STRONG>Description:</STRONG></DT>
<DD><DL>
<DD>Topocentric apparent RA,Dec of a Solar-System object whose
      heliocentric orbital elements are known.

</DD>
</DL>
      
<BR>   
   
</DD>
<DT><STRONG>Invocation:</STRONG></DT>
<DD><DL>
<DD><TT>      void palPlante ( double date, double elong, double phi, int jform,
                       double epoch, double orbinc, double anode, double perih,
                       double aorq, double e, double aorl, double dm,
                       double <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$*$"></SPAN>ra, double <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$*$"></SPAN>dec, double <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$*$"></SPAN>r, 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>
         TT MJD of observation (JD-2400000.5)
      
      
</DD>
<DT><STRONG>
         elong = double (Given)
      </STRONG></DT>
<DD>
         Observer<TT>'</TT>s east longitude (radians)
      
      
</DD>
<DT><STRONG>
         phi = double (Given)
      </STRONG></DT>
<DD>
         Observer<TT>'</TT>s geodetic latitude (radians)
      
      
</DD>
<DT><STRONG>
         jform = int (Given)
      </STRONG></DT>
<DD>
         Element set actually returned (1-3; Note 6)
      
      
</DD>
<DT><STRONG>
         epoch = double (Given)
      </STRONG></DT>
<DD>
         Epoch of elements (TT MJD)
      
      
</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>
         ra = double <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$*$"></SPAN> (Returned)
      </STRONG></DT>
<DD>
         Topocentric apparent RA (radians)
      
      
</DD>
<DT><STRONG>
         dec = double <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$*$"></SPAN> (Returned)
      </STRONG></DT>
<DD>
         Topocentric apparent Dec (radians)
      
      
</DD>
<DT><STRONG>
         r = double <SPAN CLASS="MATH"><IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img1.png"
 ALT="$*$"></SPAN> (Returned)
      </STRONG></DT>
<DD>
         Distance from observer (AU)
      
      
</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 longitude and latitude allow correction for geocentric
           parallax.  This is usually a small effect, but can become
           important for near-Earth asteroids.  Geocentric positions can be
           generated by appropriate use of routines palEpv (or palEvp) and
           palUe2pv.

<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>Two important sources for orbital elements are Horizons, operated
           by the Jet Propulsion Laboratory, Pasadena, and the Minor Planet
           Center, operated by the Center for Astrophysics, Harvard.

<P>
</LI>
</UL>
      
<BR>
The JPL Horizons elements (heliocentric, J2000 ecliptic and
        equinox) correspond to SLALIB arguments as follows.

<P>
Major planets:

<P>
JFORM  = 1
          EPOCH  = JDCT-2400000.5
          ORBINC = IN (in radians)
          ANODE  = OM (in radians)
          PERIH  = OM<SPAN CLASS="MATH"><IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.png"
 ALT="$+$"></SPAN>W (in radians)
          AORQ   = A
          E      = EC
          AORL   = MA<SPAN CLASS="MATH"><IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.png"
 ALT="$+$"></SPAN>OM<SPAN CLASS="MATH"><IMG
 WIDTH="18" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.png"
 ALT="$+$"></SPAN>W (in radians)
          DM     = N (in radians)

<P>
Epoch of osculation = JDCT-2400000.5

<P>
Minor planets:

<P>
JFORM  = 2
          EPOCH  = JDCT-2400000.5
          ORBINC = IN (in radians)
          ANODE  = OM (in radians)
          PERIH  = W (in radians)
          AORQ   = A
          E      = EC
          AORL   = MA (in radians)

<P>
Epoch of osculation = JDCT-2400000.5

<P>
Comets:

<P>
JFORM  = 3
          EPOCH  = Tp-2400000.5
          ORBINC = IN (in radians)
          ANODE  = OM (in radians)
          PERIH  = W (in radians)
          AORQ   = QR
          E      = EC

<P>
Epoch of osculation = JDCT-2400000.5

<P>
The MPC elements correspond to SLALIB arguments as follows.

<P>
Minor planets:

<P>
JFORM  = 2
          EPOCH  = Epoch-2400000.5
          ORBINC = Incl. (in radians)
          ANODE  = Node (in radians)
          PERIH  = Perih. (in radians)
          AORQ   = a
          E      = e
          AORL   = M (in radians)

<P>
Epoch of osculation = Epoch-2400000.5

<P>
Comets:

<P>
JFORM  = 3
          EPOCH  = T-2400000.5
          ORBINC = Incl. (in radians)
          ANODE  = Node. (in radians)
          PERIH  = Perih. (in radians)
          AORQ   = q
          E      = e

<P>
Epoch of osculation = Epoch-2400000.5

</DD>
</DL>
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