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authorJoseph Hunkeler <jhunkeler@gmail.com>2015-03-04 21:21:30 -0500
committerJoseph Hunkeler <jhunkeler@gmail.com>2015-03-04 21:21:30 -0500
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+<H2><A NAME="SECTION0004131000000000000000">SLA_PERTEL - Perturbed Orbital Elements</A>
+<A NAME="xref_SLA_PERTEL">&#160;</A><A NAME="SLA_PERTEL">&#160;</A>
+</H2>
+ <DL>
+<DT><STRONG>ACTION:</STRONG>
+<DD>Update the osculating elements of an asteroid or comet by
+applying planetary perturbations.
+<P> <DT><STRONG>CALL:</STRONG>
+<DD><TT>CALL sla_PERTEL (
+ JFORM, DATE0, DATE1,
+ EPOCH0, ORBI0, ANODE0, PERIH0, AORQ0, E0, AM0,
+ EPOCH1, ORBI1, ANODE1, PERIH1, AORQ1, E1, AM1,
+ JSTAT)</TT>
+<P> </DL>
+<P> <DL>
+<DT><STRONG>GIVEN (format and dates):</STRONG>
+<DD>
+<BR>
+<TABLE CELLPADDING=3>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>JFORM</EM></TD>
+<TH ALIGN="LEFT"><B>I</B></TH>
+<TD ALIGN="LEFT" NOWRAP>choice of element set (2 or 3; Note&nbsp;1)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DATE0</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>date of osculation (TT MJD) for the given</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
+<TD ALIGN="LEFT"><B></B></TD>
+<TD ALIGN="LEFT" NOWRAP> elements</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DATE1</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>date of osculation (TT MJD) for the updated</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
+<TD ALIGN="LEFT"><B></B></TD>
+<TD ALIGN="LEFT" NOWRAP> elements</TD>
+</TR>
+</TABLE></DL>
+<P> <DL>
+<DT><STRONG>GIVEN (the unperturbed elements):</STRONG>
+<DD>
+<BR>
+<TABLE CELLPADDING=3>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>EPOCH0</EM></TD>
+<TH ALIGN="LEFT"><B>D</B></TH>
+<TD ALIGN="LEFT" NOWRAP>epoch of the given element set
+(<I>t<SUB>0</SUB></I> or <I>T</I>, TT MJD;</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
+<TD ALIGN="LEFT"><B></B></TD>
+<TD ALIGN="LEFT" NOWRAP> Note&nbsp;2)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ORBI0</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>ANODE0</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>PERIH0</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>argument of perihelion
+(<IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img101.gif"
+ ALT="$\omega$">, radians)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>AORQ0</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>E0</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>AM0</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>mean anomaly (<I>M</I>, radians, JFORM=2 only)</TD>
+</TR>
+</TABLE></DL>
+<P> <DL>
+<DT><STRONG>RETURNED (the updated elements):</STRONG>
+<DD>
+<BR>
+<TABLE CELLPADDING=3>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>EPOCH1</EM></TD>
+<TH ALIGN="LEFT"><B>D</B></TH>
+<TD ALIGN="LEFT" NOWRAP>epoch of the updated element set
+(<I>t<SUB>0</SUB></I> or <I>T</I>,</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
+<TD ALIGN="LEFT"><B></B></TD>
+<TD ALIGN="LEFT" NOWRAP> TT MJD; Note&nbsp;2)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ORBI1</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>ANODE1</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>PERIH1</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>argument of perihelion
+(<IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img101.gif"
+ ALT="$\omega$">, radians)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>AORQ1</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>E1</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>AM1</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>mean anomaly (<I>M</I>, radians, JFORM=2 only)</TD>
+</TR>
+</TABLE></DL>
+<P> <DL>
+<DT><STRONG>RETURNED (status flag):</STRONG>
+<DD>
+<BR>
+<TABLE CELLPADDING=3>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>JSTAT</EM></TD>
+<TH ALIGN="LEFT"><B>I</B></TH>
+<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> +102 = warning, distant epoch</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
+<TD ALIGN="LEFT"><B></B></TD>
+<TD ALIGN="LEFT" NOWRAP> +101 = warning, large timespan
+(&gt;100 years)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
+<TD ALIGN="LEFT"><B></B></TD>
+<TD ALIGN="LEFT" NOWRAP> +1 to +8 = coincident with major planet
+(Note&nbsp;6)</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 E0</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
+<TD ALIGN="LEFT"><B></B></TD>
+<TD ALIGN="LEFT" NOWRAP> -3 = illegal AORQ0</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
+<TD ALIGN="LEFT"><B></B></TD>
+<TD ALIGN="LEFT" NOWRAP> -4 = internal error</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>Two different element-format options are supported, as follows. <BR>
+JFORM=2, suitable for minor planets:
+<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>2.
+<DD>DATE0, DATE1, EPOCH0 and EPOCH1 are all instants of time in
+ the TT timescale (formerly Ephemeris Time, ET), expressed
+ as Modified Julian Dates (JD-2400000.5).
+ <UL>
+<LI> DATE0 is the instant at which the given
+ (<I>i.e.</I> unperturbed) osculating elements are correct.
+<LI> DATE1 is the specified instant at which the updated osculating
+ elements are correct.
+<LI> EPOCH0 and EPOCH1 will be the same as DATE0 and DATE1
+ (respectively) for the JFORM=2 case, normally used for minor
+ planets. For the JFORM=3 case, the two epochs will refer to
+ perihelion passage and so will not, in general, be the same as
+ DATE0 and/or DATE1 though they may be similar to one another.
+ </UL>
+ <DT>3.
+<DD>The elements are with respect to the J2000 ecliptic and mean equinox.
+ <DT>4.
+<DD>Unused elements (AM0 and AM1 for JFORM=3) are not accessed.
+ <DT>5.
+<DD>See the sla_PERTUE routine for details of the algorithm used.
+ <DT>6.
+<DD>This routine is not intended to be used for major planets, which
+ is why JFORM=1 is not available and why there is no opportunity
+ to specify either the longitude of perihelion or the daily
+ motion. However, if JFORM=2 elements are somehow obtained for a
+ major planet and supplied to the routine, sensible results will,
+ in fact, be produced. This happens because the sla_PERTUE routine
+ that is called to perform the calculations checks the separation
+ between the body and each of the planets and interprets a
+ suspiciously small value (0.001&nbsp;AU) as an attempt to apply it to
+ the planet concerned. If this condition is detected, the
+ contribution from that planet is ignored, and the status is set to
+ the planet number (Mercury=1,...,Neptune=8) as a warning.
+ </DL></DL>
+<P> <DL>
+<DT><STRONG>REFERENCE:</STRONG>
+<DD>Sterne, Theodore E., <I>An Introduction to Celestial Mechanics,</I>
+Interscience Publishers, 1960. Section 6.7, p199.
+ </DL>
+<BR> <HR>
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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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