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<H2><A NAME="SECTION0004137000000000000000">SLA_POLMO - Polar Motion</A>
<A NAME="xref_SLA_POLMO"> </A><A NAME="SLA_POLMO"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Polar motion: correct site longitude and latitude for polar
motion and calculate azimuth difference between celestial and
terrestrial poles.
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_POLMO (ELONGM, PHIM, XP, YP, ELONG, PHI, DAZ)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ELONGM</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>mean longitude of the site (radians, east +ve)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PHIM</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>mean geodetic latitude of the site (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>XP</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>polar motion <I>x</I>-coordinate (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>YP</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>polar motion <I>y</I>-coordinate (radians)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ELONG</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>true longitude of the site (radians, east +ve)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PHI</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>true geodetic latitude of the site (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DAZ</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>azimuth correction (terrestrial-celestial, radians)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>``Mean'' longitude and latitude are the (fixed) values for the
site's location with respect to the IERS terrestrial reference
frame; the latitude is geodetic. TAKE CARE WITH THE LONGITUDE
SIGN CONVENTION. The longitudes used by the present routine
are east-positive, in accordance with geographical convention
(and right-handed). In particular, note that the longitudes
returned by the sla_OBS routine are west-positive, following
astronomical usage, and must be reversed in sign before use in
the present routine.
<DT>2.
<DD>XP and YP are the (changing) coordinates of the Celestial
Ephemeris Pole with respect to the IERS Reference Pole.
XP is positive along the meridian at longitude <IMG WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img1.gif"
ALT="$0^{\circ}$">, and YP is positive along the meridian at longitude
<IMG WIDTH="34" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img139.gif"
ALT="$270^\circ$"> (<I>i.e.</I> <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img22.gif"
ALT="$90^{\circ}$"> west). Values for XP,YP can
be obtained from IERS circulars and equivalent publications;
the maximum amplitude observed so far is about
<IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
SRC="img32.gif"
ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$"> .
<DT>3.
<DD>``True'' longitude and latitude are the (moving) values for
the site's location with respect to the celestial ephemeris
pole and the meridian which corresponds to the Greenwich
apparent sidereal time. The true longitude and latitude
link the terrestrial coordinates with the standard celestial
models (for precession, nutation, sidereal time <I>etc</I>).
<DT>4.
<DD>The azimuths produced by sla_AOP and sla_AOPQK are with
respect to due north as defined by the Celestial Ephemeris
Pole, and can therefore be called ``celestial azimuths''.
However, a telescope fixed to the Earth measures azimuth
essentially with respect to due north as defined by the
IERS Reference Pole, and can therefore be called ``terrestrial
azimuth''. Uncorrected, this would manifest itself as a
changing ``azimuth zero-point error''. The value DAZ is the
correction to be added to a celestial azimuth to produce
a terrestrial azimuth.
<DT>5.
<DD>The present routine is rigorous. For most practical
purposes, the following simplified formulae provide an
adequate approximation: <BR>
<BR>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP><TT>ELONG</TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>=</TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>ELONGM+XP*COS(ELONGM)-YP*SIN(ELONGM)</TT></TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP><TT>PHI </TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>=</TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>PHIM+(XP*SIN(ELONGM)+YP*COS(ELONGM))*TAN(PHIM)</TT></TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP><TT>DAZ </TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>=</TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>-SQRT(XP*XP+YP*YP)*COS(ELONGM-ATAN2(XP,YP))/COS(PHIM)</TT></TD>
</TR>
</TABLE> <BR>
<BR>
<BR>
An alternative formulation for DAZ is:
<BR>
<BR>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP><TT>X </TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>=</TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>COS(ELONGM)*COS(PHIM)</TT></TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP><TT>Y </TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>=</TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>SIN(ELONGM)*COS(PHIM)</TT></TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT" NOWRAP><TT>DAZ</TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>=</TT></TD>
<TD ALIGN="LEFT" NOWRAP><TT>ATAN2(-X*YP-Y*XP,X*X+Y*Y)</TT></TD>
</TR>
</TABLE></DL></DL>
<P> <DL>
<DT><STRONG>REFERENCE:</STRONG>
<DD>Seidelmann, P.K. (ed), 1992. <I>Explanatory
Supplement to the Astronomical Almanac,</I> ISBN 0-935702-68-7,
sections 3.27, 4.25, 4.52.
</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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