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<H2><A NAME="SECTION0004131000000000000000">SLA_PERTEL - Perturbed Orbital Elements</A>
<A NAME="xref_SLA_PERTEL"> </A><A NAME="SLA_PERTEL"> </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 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 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 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
(>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 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 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>
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<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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