[pycalcal] push by enrico.spinielli - coord transf formulae in LaTeX on 2010-02-14 15:22 GMT

[pyca...@googlecode.com]

Revision: 55463377bb
Author: Enrico Spinielli <enrico.s...@gmail.com>
Date: Sun Feb 14 07:22:45 2010
Log: coord transf formulae in LaTeX
http://code.google.com/p/pycalcal/source/detail?r=55463377bb

Modified:
/pycalcal.nw

=======================================
--- /pycalcal.nw Sat Feb 13 07:16:26 2010
+++ /pycalcal.nw Sun Feb 14 07:22:45 2010
@@ -26,6 +26,14 @@
% smallcode: Set code in LaTeX \small font instead of \normalsize.
\noweboptions{externalindex,webnumbering,longxref,longchunks,smallcode}

+% example usage: 12^h 45^m 23^s (\showclock{12}{45}{23}).
+% TODO: maybe should not display h (or h and m) if zero
+\newcommand{\showclock}[3]{$#1^{h} #2^{m} #3^{s}$}
+
+% example usage: 12^\circ 45' 23''.56 (\showdegrees{12}{45}{23}).
+% TODO: maybe should not display \circ (or \circ and ') if zero
+% Consider kerning decimal of seconds if presenr
+\newcommand{\showdegrees}[3]{#1^{\circ}\,#2'\,#3''}

\newcommand*{\manualmark}{%
\if@chapter\let\chaptermark\@gobble\fi
@@ -3204,7 +3212,9 @@
equinox of the date (or to the mean equator and mean equinox of the
date.)

\end{description}
-\subsection{$Alt-az$ Coordinate systems}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{$Alt-az$ Coordinate system}
\label{sec:alt-az}
The alt-az is a topocentric (i.e. as seen from the observer's
place on the Earth's surface) celestial coordinate system.
@@ -3247,7 +3257,7 @@


%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{$HA-dec$ Coordinate systems}
+\subsection{$HA-dec$ Coordinate system}
\label{sec:HA-dec}
A system of celestial coordinates which is fixed on the sky and
independent of the observer's time and place can be defined by
@@ -3272,7 +3282,8 @@
It is measured westwards in hours, 0h-24h, since the Earth rotates 360° in
24 hours.


-\subsection{$RA-dec$ Coordinate systems}
+%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{$RA-dec$ Coordinate system}
\label{sec:RA-dec}
Figure~\ref{fig:RA-DEC}\ displays the celestial sphere and the RA-dec
coordinate system (also named second equtorial).
@@ -3313,20 +3324,35 @@
\rule{\textwidth}{0.005in}
\end{figure}

-<<fig_coord_transform.gv>>=
-# genrate w/ twopi -Tpng fig_coord_transform.gv > fig_coord_transform.png
-digraph finite_state_machine {
- ranksep=3;
- ratio=auto;
- node [shape = doublecircle]; equatorial;
- node [shape = circle, fixedsize = true, width = 1.5];
- equatorial -> galactic [ labeldistance=3, headlabel = "1" ];
- galactic -> equatorial [ labeldistance=3, headlabel = "2" ];
- equatorial -> ecliptical [ labeldistance=3, headlabel = "3" ];
- ecliptical -> equatorial [ labeldistance=3, headlabel = "4" ];
- equatorial -> horizontal [ labeldistance=3, headlabel = "5" ];
- horizontal -> equatorial [ labeldistance=3, headlabel = "6" ];
-}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Galactic Coordinate system}
+\label{sec:galactic}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Coordinates Transformation}
+Ecliptical from equatorial:
+\begin{eqnarray}
+ \label{eq:equ2ecl}
+ \tan \lambda &=& \frac{\sin \alpha\ \cos \varepsilon +
+ \tan \delta\ \sin \varepsilon}{\cos \alpha} \\
+ \sin \beta &=& \sin \delta\ \cos \varepsilon - \cos \delta\ \sin
\varepsilon\ \sin \alpha
+\end{eqnarray}
+where
+\begin{description}
+\item[$\lambda$] is the ecliptical longitude, positive if north of the
ecliptic,
+ negative if south;
+\item[$\beta$] is the ecliptical latitude, positive if north of the
ecliptic,
+ negative if south;
+\item[$\alpha$] is the right ascension;
+\item[$\varepsilon$] is the obliquity of the ecliptic, that is the angle
between
+ ecliptic and the celestial equator~\footnote{if \emph{apparent} right
+ ascension and declination are used, i.e. affected by aberration and
+ nutation), then the \emph{true} obliquity should be used, see
+ eq.~\ref{eq:trueobliquity}; for \emph{mean} RA and declination we can
use
+ mean obliquity from eq.~\ref{eq:meanobliquity}};
+\item[$\delta$] is the declination, positive if north of the celestial
equator,
+ negative if south;
+\end{description}

<<time and astronomy>>=
######################
@@ -3685,6 +3711,13 @@
"""Return Julian centuries since 2000 at moment tee."""
return (dynamical_from_universal(tee) - J2000) / mpf(36525)

+@
+The \emph{mean} obliquity is defined by the following formula:
+\begin{equation}
+ \label{eq:meanobliquity}
+ \varepsilon_0 = \showdegrees{23}{26}{21.448} - 46''\!\!.8150 T -
0''.00059 T^2 + 0''.001813 T^3
+\end{equation}
+<<time and astronomy>>=
# see lines 2872-2880 in calendrica-3.0.cl
def `obliquity(tee):
"""Return (mean) obliquity of ecliptic at moment tee."""