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authorJoseph Hunkeler <jhunkeler@gmail.com>2015-03-04 21:21:30 -0500
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+<H2><A NAME="SECTION0004122000000000000000">SLA_OAP - Observed to Apparent</A>
+<A NAME="xref_SLA_OAP">&#160;</A><A NAME="SLA_OAP">&#160;</A>
+</H2>
+ <DL>
+<DT><STRONG>ACTION:</STRONG>
+<DD>Observed to apparent place.
+<DT><STRONG>CALL:</STRONG>
+<DD><TT>CALL sla_OAP (
+ TYPE, OB1, OB2, DATE, DUT, ELONGM, PHIM,
+ HM, XP, YP, TDK, PMB, RH, WL, TLR, RAP, DAP)</TT>
+<P> </DL>
+<P> <DL>
+<DT><STRONG>GIVEN:</STRONG>
+<DD>
+<BR>
+<TABLE CELLPADDING=3>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>TYPE</EM></TD>
+<TH ALIGN="LEFT"><B>C*(*)</B></TH>
+<TD ALIGN="LEFT" NOWRAP>type of coordinates - `R', `H' or `A' (see below)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>OB1</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>observed Az, HA or RA (radians; Az is N=0, E=<IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img22.gif"
+ ALT="$90^{\circ}$">)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>OB2</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>observed zenith distance or <IMG WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ SRC="img23.gif"
+ ALT="$\delta$"> (radians)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DATE</EM></TD>
+<TD ALIGN="LEFT"><B>D </B></TD>
+<TD ALIGN="LEFT" NOWRAP>UTC date/time (Modified Julian Date, JD-2400000.5)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DUT</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP><IMG WIDTH="16" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ SRC="img19.gif"
+ ALT="$\Delta$">UT: UT1-UTC (UTC seconds)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ELONGM</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>observer's mean longitude (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>observer's mean geodetic latitude (radians)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>HM</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>observer's height above sea level (metres)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>XP,YP</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>polar motion <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img20.gif"
+ ALT="$[\,x,y\,]$"> coordinates (radians)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>TDK</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>local ambient temperature (degrees K; std=273.155D0)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PMB</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>local atmospheric pressure (mB; std=1013.25D0)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RH</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>local relative humidity (in the range 0D0-1D0)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>WL</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>effective wavelength (<IMG WIDTH="26" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
+ SRC="img21.gif"
+ ALT="$\mu{\rm m}$">, <I>e.g.</I> 0.55D0)</TD>
+</TR>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>TLR</EM></TD>
+<TD ALIGN="LEFT"><B>D</B></TD>
+<TD ALIGN="LEFT" NOWRAP>tropospheric lapse rate (degrees K per metre,
+<I>e.g.</I> 0.0065D0)</TD>
+</TR>
+</TABLE></DL>
+<P> <DL>
+<DT><STRONG>RETURNED:</STRONG>
+<DD>
+<BR>
+<TABLE CELLPADDING=3>
+<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RAP,DAP</EM></TD>
+<TH ALIGN="LEFT"><B>D</B></TH>
+<TD ALIGN="LEFT" NOWRAP>geocentric apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img3.gif"
+ ALT="$[\,\alpha,\delta\,]$"></TD>
+</TR>
+</TABLE></DL>
+<P> <DL>
+<DT><STRONG>NOTES:</STRONG>
+<DD><DL COMPACT>
+<DT>1.
+<DD>Only the first character of the TYPE argument is significant.
+`R' or `r' indicates that OBS1 and OBS2 are the observed Right
+Ascension and Declination; `H' or `h' indicates that they are
+ Hour Angle (west +ve) and Declination; anything else (`A' or
+ `a' is recommended) indicates that OBS1 and OBS2 are Azimuth
+ (north zero, east is <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img22.gif"
+ ALT="$90^{\circ}$">) and Zenith Distance. (Zenith
+ distance is used rather than elevation in order to reflect the
+ fact that no allowance is made for depression of the horizon.)
+ <DT>2.
+<DD>The accuracy of the result is limited by the corrections for
+ refraction. Providing the meteorological parameters are
+ known accurately and there are no gross local effects, the
+ predicted azimuth and elevation should be within about
+<P> <IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img25.gif"
+ ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$"> for <IMG WIDTH="56" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
+ SRC="img26.gif"
+ ALT="$\zeta<70^{\circ}$">. Even
+ at a topocentric zenith distance of
+ <IMG WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img22.gif"
+ ALT="$90^{\circ}$">, the accuracy in elevation should be better than
+ 1&nbsp;arcminute; useful results are available for a further
+ <IMG WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img27.gif"
+ ALT="$3^{\circ}$">, beyond which the sla_REFRO routine returns a
+ fixed value of the refraction. The complementary
+ routines sla_AOP (or sla_AOPQK) and sla_OAP (or sla_OAPQK)
+ are self-consistent to better than 1&nbsp;microarcsecond all over
+ the celestial sphere.
+ <DT>3.
+<DD>It is advisable to take great care with units, as even
+ unlikely values of the input parameters are accepted and
+ processed in accordance with the models used.
+ <DT>4.
+<DD><I>Observed</I> <IMG WIDTH="66" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img28.gif"
+ ALT="$[\,Az,El~]$"> means the position that would be seen by a
+ perfect theodolite located at the observer. This is
+ related to the observed <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img29.gif"
+ ALT="$[\,h,\delta\,]$"> via the standard rotation, using
+ the geodetic latitude (corrected for polar motion), while the
+ observed HA and RA are related simply through the local
+ apparent ST. <I>Observed</I> <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img3.gif"
+ ALT="$[\,\alpha,\delta\,]$"> or <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img29.gif"
+ ALT="$[\,h,\delta\,]$"> thus means the
+ position that would be seen by a perfect equatorial located
+ at the observer and with its polar axis aligned to the
+ Earth's axis of rotation (<I>n.b.</I> not to the refracted pole).
+ By removing from the observed place the effects of
+ atmospheric refraction and diurnal aberration, the
+ geocentric apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img3.gif"
+ ALT="$[\,\alpha,\delta\,]$"> is obtained.
+ <DT>5.
+<DD>Frequently, <I>mean</I> rather than <I>apparent</I>
+ <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img3.gif"
+ ALT="$[\,\alpha,\delta\,]$"> will be required,
+ in which case further transformations will be necessary. The
+ sla_AMP <I>etc.</I> routines will convert
+ the apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img3.gif"
+ ALT="$[\,\alpha,\delta\,]$"> produced
+ by the present routine into an FK5 J2000 mean place, by
+ allowing for the Sun's gravitational lens effect, annual
+ aberration, nutation and precession. Should FK4 B1950
+ coordinates be needed, the routines sla_FK524 <I>etc.</I> will also
+ need to be applied.
+ <DT>6.
+<DD>To convert to apparent <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img3.gif"
+ ALT="$[\,\alpha,\delta\,]$"> the coordinates read from a
+ real telescope, corrections would have to be applied for
+ encoder zero points, gear and encoder errors, tube flexure,
+ the position of the rotator axis and the pointing axis
+ relative to it, non-perpendicularity between the mounting
+ axes, and finally for the tilt of the azimuth or polar axis
+ of the mounting (with appropriate corrections for mount
+ flexures). Some telescopes would, of course, exhibit other
+ properties which would need to be accounted for at the
+ appropriate point in the sequence.
+ <DT>7.
+<DD>The star-independent apparent-to-observed-place parameters
+ in AOPRMS may be computed by means of the sla_AOPPA routine.
+ If nothing has changed significantly except the time, the
+ sla_AOPPAT routine may be used to perform the requisite
+ partial recomputation of AOPRMS.
+ <DT>8.
+<DD>The DATE argument is UTC expressed as an MJD. This is,
+ strictly speaking, wrong, because of leap seconds. However,
+ as long as the <IMG WIDTH="16" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ SRC="img19.gif"
+ ALT="$\Delta$">UT and the UTC are consistent there
+ are no difficulties, except during a leap second. In this
+ case, the start of the 61st second of the final minute should
+ begin a new MJD day and the old pre-leap <IMG WIDTH="16" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ SRC="img19.gif"
+ ALT="$\Delta$">UT should
+ continue to be used. As the 61st second completes, the MJD
+ should revert to the start of the day as, simultaneously,
+ the <IMG WIDTH="16" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ SRC="img19.gif"
+ ALT="$\Delta$">UT changes by one second to its post-leap new value.
+ <DT>9.
+<DD>The <IMG WIDTH="16" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ SRC="img19.gif"
+ ALT="$\Delta$">UT (UT1-UTC) is tabulated in IERS circulars and
+ elsewhere. It increases by exactly one second at the end of
+ each UTC leap second, introduced in order to keep <IMG WIDTH="16" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
+ SRC="img19.gif"
+ ALT="$\Delta$">UT
+ within <IMG WIDTH="15" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
+ SRC="img30.gif"
+ ALT="$\pm$"><IMG WIDTH="24" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img31.gif"
+ ALT="$0^{\rm s}\hspace{-0.3em}.9$">. <DT>10.
+<DD>IMPORTANT - TAKE CARE WITH THE LONGITUDE SIGN CONVENTION. The
+ longitude required by the present routine is <B>east-positive</B>,
+ in accordance with geographical convention (and right-handed).
+ In particular, note that the longitudes returned by the
+ sla_OBS routine are west-positive (as in the <I>Astronomical
+ Almanac</I> before 1984) and must be reversed in sign before use
+ in the present routine.
+ <DT>11.
+<DD>The polar coordinates XP,YP can be obtained from IERS
+ circulars and equivalent publications. The
+ maximum amplitude is about
+ <IMG WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
+ SRC="img32.gif"
+ ALT="$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.3$"> . If XP,YP values
+ are unavailable, use XP=YP=0D0. See page B60 of the 1988
+ <I>Astronomical Almanac</I> for a definition of the two angles.
+ <DT>12.
+<DD>The height above sea level of the observing station, HM,
+ can be obtained from the <I>Astronomical Almanac</I> (Section J
+ in the 1988 edition), or via the routine sla_OBS. If P,
+ the pressure in mB, is available, an adequate
+ estimate of HM can be obtained from the following expression:
+ <BLOCKQUOTE><TT>HM=-29.3D0*TSL*LOG(P/1013.25D0)</TT>
+ </BLOCKQUOTE>
+ where TSL is the approximate sea-level air temperature in degrees K
+ (see <I>Astrophysical Quantities</I>, C.W.Allen, 3rd&nbsp;edition,
+ &#167;52). Similarly, if the pressure P is not known,
+ it can be estimated from the height of the observing
+ station, HM as follows:
+ <BLOCKQUOTE><TT>P=1013.25D0*EXP(-HM/(29.3D0*TSL))</TT>
+ </BLOCKQUOTE>
+ Note, however, that the refraction is proportional to the
+ pressure and that an accurate P value is important for
+ precise work.
+ <DT>13.
+<DD>The azimuths <I>etc.</I> used by the present routine are with
+ respect to the celestial pole. Corrections from the terrestrial pole
+ can be computed using sla_POLMO.
+ </DL></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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