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<H2><A NAME="SECTION00044000000000000000">SLA_ALTAZ - Velocities <I>etc.</I> for Altazimuth Mount</A>
<A NAME="xref_SLA_ALTAZ"> </A><A NAME="SLA_ALTAZ"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Positions, velocities and accelerations for an altazimuth
telescope mount tracking a star (double precision).
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_ALTAZ (
HA, DEC, PHI,
AZ, AZD, AZDD, EL, ELD, ELDD, PA, PAD, PADD)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>HA</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>hour angle</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>DEC</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>declination</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PHI</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>observatory latitude</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>AZ</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TD ALIGN="LEFT" NOWRAP>azimuth</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>AZD</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>azimuth velocity</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>AZDD</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>azimuth acceleration</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>EL</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>elevation</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ELD</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>elevation velocity</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ELDD</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>elevation acceleration</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PA</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>parallactic angle</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PAD</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>parallactic angle velocity</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PADD</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>parallactic angle acceleration</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>Natural units are used throughout. HA, DEC, PHI, AZ, EL
and ZD are in radians. The velocities and accelerations
assume constant declination and constant rate of change of
hour angle (as for tracking a star); the units of AZD, ELD
and PAD are radians per radian of HA, while the units of AZDD,
ELDD and PADD are radians per radian of HA squared. To
convert into practical degree- and second-based units:
<P> <DIV ALIGN="CENTER">
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="RIGHT" NOWRAP>angles</TD>
<TD ALIGN="LEFT" NOWRAP><IMG WIDTH="66" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img9.gif"
ALT="$\times 360/2\pi$"></TD>
<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img10.gif"
ALT="$\rightarrow$"></TD>
<TD ALIGN="LEFT" NOWRAP>degrees</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="RIGHT" NOWRAP>velocities</TD>
<TD ALIGN="LEFT" NOWRAP><IMG WIDTH="178" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img11.gif"
ALT="$\times (2\pi/86400) \times (360/2\pi)$"></TD>
<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img10.gif"
ALT="$\rightarrow$"></TD>
<TD ALIGN="LEFT" NOWRAP>degree/sec</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="RIGHT" NOWRAP>accelerations</TD>
<TD ALIGN="LEFT" NOWRAP><IMG WIDTH="186" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
SRC="img12.gif"
ALT="$\times (2\pi/86400)^2 \times (360/2\pi)$"></TD>
<TD ALIGN="CENTER" NOWRAP><IMG WIDTH="19" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img10.gif"
ALT="$\rightarrow$"></TD>
<TD ALIGN="LEFT" NOWRAP>degree/sec/sec</TD>
</TR>
</TABLE></DIV>
<P>
Note that the seconds here are sidereal rather than SI. One
sidereal second is about 0.99727 SI seconds.
<P>
The velocity and acceleration factors assume the sidereal
tracking case. Their respective numerical values are (exactly)
1/240 and (approximately) 1/3300236.9.
<DT>2.
<DD>Azimuth is returned in the range <IMG WIDTH="50" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img13.gif"
ALT="$[\,0,2\pi\,]$">; north is zero,
and east is <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img14.gif"
ALT="$+\pi/2$">. Elevation and parallactic angle are
returned in the range <IMG WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img15.gif"
ALT="$\pm\pi/2$">. Position angle is +ve
for a star west of the meridian and is the angle NP-star-zenith.
<DT>3.
<DD>The latitude is geodetic as opposed to geocentric. The
hour angle and declination are topocentric. Refraction and
deficiencies in the telescope mounting are ignored. The
purpose of the routine is to give the general form of the
quantities. The details of a real telescope could profoundly
change the results, especially close to the zenith.
<DT>4.
<DD>No range checking of arguments is carried out.
<DT>5.
<DD>In applications which involve many such calculations, rather
than calling the present routine it will be more efficient to
use inline code, having previously computed fixed terms such
as sine and cosine of latitude, and (for tracking a star)
sine and cosine of declination.
</DL></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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