Changeset 1666 for trunk/doc/pslib/psLibADD.tex

Timestamp:

Aug 31, 2004, 5:47:27 PM (22 years ago)

Author:

Paul Price

Message:

Fleshed out the celestial coordinate conversions, including finding
the best pole values to use, checking the rotation formulae, and
dreaming up a few test cases.

File:

• trunk/doc/pslib/psLibADD.tex (modified) (4 diffs)

trunk/doc/pslib/psLibADD.tex

@@ -1 @@
-%%% $Id: psLibADD.tex,v 1.31 2004-08-25 04:36:56 price Exp $
+%%% $Id: psLibADD.tex,v 1.32 2004-09-01 03:47:27 price Exp $
 \documentclass[panstarrs]{panstarrs}
 
@@ -49 +49 @@
 FFTW                                & {\tt http://www.fftw.org} (Fastest Fourier Transform in the West) \\ \hline
 FITS Projection Article             &  {\tt http://www.cv.nrao.edu/fits/documents/wcs/wcs.all.ps}{Greisen \&
-Calabretta (1995, ADASS, 4, 233)} \\ \hline
+Calabretta (1995, ADASS, 4, 233)} \\
+Hipparcos and Tycho Catalogues      & \code{http://astro.estec.esa.nl/Hipparcos/CATALOGUE_VOL1/catalog_vol1.html} \\
+Zombeck                             & ``Handbook of Space Astronomy and Astrophysics'', second edition, \code{http://ads.harvard.edu/books/hsaa/toc.html} \\
+\hline
 \DocumentsEnd
 
@@ -1145 +1148 @@
 
 The relevant trigonometric relationships are:
-\begin{eqnarray}
-\sin \theta                        = \cos \delta \sin \delta_p \sin (\alpha - \alpha_p) + \sin \delta \cos \delta_p
-\cos \theta \sin (\phi - \phi_p)   = \cos \delta \cos \delta_p \sin (\alpha - \alpha_p) - \sin \delta \sin \delta_p
+%
+\begin{eqnarray}
+\sin \theta                        = \sin \delta \cos \delta_p - \cos \delta \sin \delta_p \sin (\alpha - \alpha_p) 
+\cos \theta \sin (\phi - \phi_p)   = \cos \delta \cos \delta_p \sin (\alpha - \alpha_p) + \sin \delta \sin \delta_p
 \cos \theta \cos (\phi - \phi_p)   = \cos \delta \cos (\alpha - \alpha_p)
 \end{eqnarray}
@@ -1154 +1158 @@
 %
 \begin{eqnarray}
-\sin \delta                          & = & \cos \theta \sin \delta_p \sin (\phi - \phi_p) + \sin \theta \cos \delta_p \\
-\cos \delta \sin (\alpha - \alpha_p) & = & \cos \theta \cos \delta_p \sin (\phi - \phi_p) - \sin \theta \sin \delta_p \\
+\sin \delta                          & = & \sin \theta \cos \delta_p - \cos \theta \sin \delta_p \sin (\phi - \phi_p) \\
+\cos \delta \sin (\alpha - \alpha_p) & = & \cos \theta \cos \delta_p \sin (\phi - \phi_p) + \sin \theta \sin \delta_p \\
 \cos \delta \cos (\alpha - \alpha_p) & = & \cos \theta \cos (\phi - \phi_p)
 \end{eqnarray}
-%
 Since $\theta$ and $\delta$ have domains of $-\pi/2, \pi/2$, the value
 of these angles are found by applying the arcsin to the sine of these
 angles ($\theta = \arcsin \sin \theta$) which is always single-valued
-and defined.  The value of $\alpha$ (or $\phi$) is found from
-\code{atan2(y,x)}, where $y = \cos \delta \sin (\alpha - \alpha_p)$ and
-$x = \cos \delta \cos (\alpha - \alpha_p)$.   
+and defined.  The value of $\alpha-\alpha_p$ may be found from
+\code{atan2(y,x)}, where $y = \cos \delta \sin (\alpha - \alpha_p)$
+and $x = \cos \delta \cos (\alpha - \alpha_p)$; and similarly for
+$\phi-\phi_p$.
 
 \paragraph{Galactic to ICRS}
 
-\tbd{clean up these values - the transformations above need to be
-  checked for pole vs node coords}
-
-\begin{verbatim}
-*  P = 192.25       RA of galactic north pole (mean B1950.0)
-*  Q =  62.6        inclination of galactic to mean B1950.0 equator
-*  R =  33          longitude of ascending node
-
-We should precess L2,B2 coords from B1950 to epoch of interest 
-
-265.600000 -28.916667 (B1950)
-192.250000  27.400000 (B1950)
-
-266.394165 -28.936098 (J2000)
-192.859536  27.128309 (J2000)
-\end{verbatim}
-
-These will be implemented using the corresponding SLALIB functions:
-
-\begin{tabular}{ll}
-  PSLib function             & SLALIB function \\ \hline
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-  \code{psCoordinatesICRSToEcliptic()} & \code{sla_EQECL} \\
-  \code{psCoordinatesEclipticToICRS()} & \code{sla_ECLEQ} \\
-  \code{psCoordinatesICRSToGalactic()} & \code{sla_EQGAL} \\
-  \code{psCoordinatesGalacticToICRS()} & \code{sla_GALEQ} \\
-\end{tabular}
+The appropriate values, from the Hipparcos and Tycho Catalogues are:
+\begin{eqnarray}
+\alpha_p = 282.85948^\circ
+\delta_p = 62.87175^\circ
+\phi_p = 32.93192^\circ
+
+\end{eqnarray}
+
+\paragraph{Ecliptic to ICRS}
+
+The appropriate values, from Zombeck, are:
+\begin{eqnarray}
+\alpha_p = 0^\circ
+\delta_p = 23^\circ27'8''.26 - 46''.845\, T - 0''.0059\, T^2 + 0''.00181\, T^3
+\phi_p = 0^\circ
+\end{eqnarray}
+where $T$ is the time in \tbr{Julian} centuries since 1900.
+
+\paragraph{Suggested test cases}
+
+$(\alpha,\delta) = (0^\circ,0^\circ)$ transforms to Galactic
+coordinates $(l,b) = (96.337272^\circ,-60.188553^\circ)$, and Ecliptic
+coordinates $(\lambda,\beta) = (0^\circ,0^\circ)$.
+
+$(\alpha,\delta) = (0^\circ,90^\circ)$ transforms to Galactic coordinates
+$(l,b) = (122.93192^\circ,27.12825^\circ)$, and Ecliptic coordinates
+at J2000.0 (i.e., $T=1$), $(\lambda,\beta) =
+(90^\circ,66.560719^\circ)$.
+
+$(\alpha,\delta) = (180^\circ,30^\circ)$ transforms to Galactic
+coordinates $(l,b) = (195.639488^\circ,78.353806^\circ)$, and Ecliptic
+coordinates at J2100.0 (i.e., $T=2$), $(\lambda,\beta) =
+(167.072470^\circ,27.308813^\circ)$.
 
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