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% 
% MoonPhases.tex
%
% Peter Newbury
% Department of Physics and Astronomy, UBC 
% newbury@phas.ubc.ca
% Twitter @polarisdotca
% http://blogs.ubc.ca/polarisdotca
%
% 6 Sept 2011
%
% This work is supported by the Carl Wieman Science Education
% Initiative cwsei.ubc.ca.
%
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\begin{document}

\begin{center}
  \huge
  Phases of the Moon\\
\end{center}

\bigskip

\begin{tabularx}{\textwidth}[t]{@{}Xc@{}}
  Every month, the Moon appears to change shape in the sky as it goes
  through phases from new Moon to full Moon and then back to new.
  Ancient civilizations used the phases of the Moon to 
  track the passage of time.  Today's Gregorian calendar no longer
  depends on the phases of the Moon but the Islamic, Hebrew and
  Chinese cultures still base festivals and holy days on the cycles of
  the Moon.
  
  \medskip
  The more you understand the nature of the Moon's phases, the more you
  can appreciate how astronomy influences our culture and the better
  you'll be able to predict when important events like Ramadan,
  Hannukah, Easter and Lunar New Year will occur.

  \medskip
  In this tutorial, you will explore the changing geometry of the
  Sun-Earth-Moon system that produces each phase of the Moon, and then
  the connection between the geometry and the time of day the Moon rises
  and sets. 
  
  \bigskip
  {\bf Materials}  Each group of 3 partners needs a (small) Moon ball and
  a (big) Earth ball.


  &
  % Moon phases figure
  \begin{tabular}[t]{p{3in}}
    \ \\
    \includegraphics[width=3in]{Moon_phases_small}\\
    Phases of the Moon (Copyright Antonio Cidadao. Used by
    permission.)
  \end{tabular}
\end{tabularx}


\clearpage

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  %\rput{U}(0,0){\tiny Sun}
  \endpspicture}



\begin{landscape}
  {\Large Part 1: Phases of the Moon}
 
  \medskip

% adjust sketchspace to fill page
\psset{unit=25mm}
\newcommand{\moonwidth}{1in}

  Imagine your head is the Earth.  When it's your turn, stand in the
  ``sunlight'' and hold the Moon straight out at arm's length.  Be sure
  the NEAR side is always facing towards you.  Spin around slowly to
  your left and watch the Moon go through phases.

  \medskip
  Take turns holding the Moon in the sunlight to find the geometry of
  the Sun, Earth and Moon that create these phases.  Below each picture,
  {\bf sketch the geometry of the Sun, Earth and Moon} as seen from
  above.  Try to indicate the illuminated halves of the Earth and Moon.

  \medskip
  \begin{tabular}{|c|c|c|}\hline
    \rowcolor[gray]{0.8}
    \makebox[3in]{\bf Partner 1} &
    \makebox[3in]{\bf Partner 2} &
    \makebox[3in]{\bf Partner 3} \\\hline
    % top titles
    first quarter Moon &
    third quarter Moon &
    waning gibbous Moon \\
    % top graphics
    \includegraphics[width=\moonwidth]{FirstQuarter} &
    \includegraphics[width=\moonwidth]{ThirdQuarter} &
    \includegraphics[width=\moonwidth]{WaningGibbous} \\[28ex]\hline
    % bottom titles
    full Moon &
    waxing crescent Moon &
    new Moon \\
    % bottom graphics
    \includegraphics[width=\moonwidth]{FullMoon} &
    \includegraphics[width=\moonwidth]{WaxingCrescent} &
    \includegraphics[width=\moonwidth]{NewMoon}\\[28ex]\hline
  \end{tabular}

\end{landscape}
\clearpage

{\Large Part 2: Local Time on Earth}

\bigskip

Unlike the Sun which rises in the morning and sets in the evening, the
Moon rises and sets at different times during the day and night depending on its phase.

\bigskip
First we'll review how your local time is determined by the location of
the Sun in the sky.  Imagine the observer is standing on the Earth at
the location of the sticker, watching the sky.

\begin{enumerate}
  \renewcommand{\arraystretch}{2}
  %\setcounter{enumi}{12}
  \item  Hold the Earth in the ``sunlight'' with the axis (the pencil) straight up
    and down.  Rotate the  Earth until the Sun is directly over the observer.
    Complete this table:

    \begin{center}
      \begin{tabular}{|c|c|}\hline
        \makebox[2in]{\bf Local Time} & 
        \makebox[2in]{\bf Location of Sun} \\\hline
         & directly overhead \\\hline
      \end{tabular}
    \end{center}

  \item Rotate the Earth, carrying the observer towards the East,  by
    one-quarter of a rotation.  The observer will now be on the boundary
    between light and dark (day and night).

    \begin{center}
      \begin{tabular}{|c|c|}\hline
        \makebox[2in]{\bf Local Time} & 
        \makebox[2in]{\bf Location of Sun} \\\hline
        \phantom{6:00 p.m.} & on Western horizon \\\hline
      \end{tabular}
    \end{center}

  \item Rotate the Earth another $\frac{1}{4}$-turn.

    \begin{center}
      \begin{tabular}{|c|c|}\hline
        \makebox[2in]{\bf Local Time} & 
        \makebox[2in]{\bf Location of Sun} \\\hline
        &  \\\hline
      \end{tabular}
    \end{center}

  \item Rotate the Earth another $\frac{1}{4}$-turn.

    \begin{center}
      \begin{tabular}{|c|c|}\hline
        \makebox[2in]{\bf Local Time} & 
        \makebox[2in]{\bf Location of Sun} \\\hline
         & \\\hline
      \end{tabular}
    \end{center}

  \item Finally, rotate the Earth another $\frac{1}{4}$-turn.  It's noon
    again.

\end{enumerate}

\clearpage

\newcommand{\moontime}{20mm}

{\Large Part 3: Moonrise and Moonset}

\bigskip

\hyphenation{moonrise moonset}

%\begin{tabularx}{\textwidth}{|r@{\ }X|X|X|}\hline
\begin{tabularx}{\textwidth}{|c|X|X|X|}\hline
  \rowcolor[gray]{0.8}
  &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{{\bf Earth}} &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{{\bf Moon}} & 
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{{\bf Recorder}} \\
  % roles
  \rowcolor[gray]{0.8}
  &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{Partner 1} &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{Partner 2} & 
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{Partner 3} \\\hline\hline
  %
  % Set 1
  %
  1 &
  % Earth
  Hold the Earth straight up-and-down in the ``sunlight''. When you
  rotate the Earth later, remember it always rotates to the East. 
  &
  % Moon
  Hold the Moon about an arm's length from Earth and make one slow
  orbit around Earth.  Be sure the NEAR side of the Moon is always facing 
  towards the Earth. 
  &
  % Recorder
  Watch the Moon and help your partner keep the NEAR side facing towards
  the Earth.  Then record the times below.
  \\\hline

  %
  % first quarter
  %

  2 &
  % Earth
  &
  % Moon
  Move to the {\bf first quarter} Moon. &
  % Recorder

  \\\hline
  3 &
  % Earth
  Rotate the Earth until {\bf moonrise}, the moment when the Moon appears
  on the observer's Eastern horizon.
  &
  % Moon
  Help find the observer's local time.
  &
  % Recorder
  {\bf First quarter} Moon rises at\newline \underline{\hspace{\moontime}}
  \\
  & & & \\
  &
  % Earth
  Rotate the Earth until {\bf moonset}, the moment when the Moon
  disappears behind the observer's Western horizon.
  &
  % Moon
  % (continue helping)
  &
  % Recorder
  {\bf First quarter} Moon sets at \newline \underline{\hspace{\moontime}}
  \\\hline
  
  %
  % full moon
  %
  4 &
  % Earth
  &
  % Moon
  Move to {\bf full} Moon. &
  % Recorder 
  % (get ready)
  \\\hline
  5 & 
  % Earth
  Rotate the Earth until {\bf moonrise}.&
  % Moon
  Help find the observer's local time. &
  % Recorder
  {\bf Full} Moon rises at \ \underline{\hspace{\moontime}}     
  \\[4ex]
  &
  % Earth
  Rotate the Earth until {\bf moonset}. &
  % Moon
  % (keep helping)
  &
  % Recorder
  {\bf Full} Moon sets at \ \underline{\hspace{\moontime}}
  \\\hline
\end{tabularx}

\vfill
\centerline{\Large\it Everyone\ \  switch\ \  jobs}
\vfill

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Second set
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{tabularx}{\textwidth}{|c|X|X|X|}\hline
  \rowcolor[gray]{0.8}
  &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{{\bf Earth}} &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{{\bf Moon}} & 
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{{\bf Recorder}} \\
  % roles
  \rowcolor[gray]{0.8}
  &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{Partner 3} &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{Partner 1} & 
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{Partner 2} \\\hline\hline
  6 &
  % Earth
  Hold the Earth straight up-and-down in the ``sunlight''. When you
  rotate the Earth later, remember it always rotates to the East. 
  &
  % Moon
  Hold the Moon about an arm's length from Earth and make one slow
  orbit around Earth.  Be sure the NEAR side of the Moon is always facing 
  towards the Earth. 
  &
  % Recorder
  Watch the Moon and help your partner keep the NEAR side facing towards
  the Earth.  Then record the times below.
  \\\hline

  %
  % third quarter
  %
  7 &
  % Earth
  &
  % Moon
  Move to the {\bf third quarter} Moon. &
  % Recorder
  \\\hline
  8 &
  % Earth
  Rotate the Earth until {\bf moonrise}.
  &
  % Moon
  Help find the observer's local time.
  &
  % Recorder
  {\bf Third quarter} Moon rises at \ \underline{\hspace{\moontime}}
  \\
  & & & \\
  &
  % Earth
  Rotate the Earth until {\bf moonset}.
  &
  % Moon
  % (continue helping)
  &
  % Recorder
  {\bf Third quarter} Moon sets at \ \underline{\hspace{\moontime}}
  \\\hline
  
  %
  % new moon
  %
  9 &
  % Earth
  %Help the Moon move to {\bf new} Moon.
  &
  % Moon
  Move to {\bf new} Moon. &
  % Recorder 
  % (get ready)
  \\\hline
  10 & 
  % Earth
  Rotate the Earth until {\bf moonrise}. &
  % Moon
  Help find the observer's local time. &
  % Recorder
  {\bf New} Moon rises at \ \underline{\hspace{\moontime}}     
  \\[3ex]
  &
  % Earth
  Rotate the Earth until {\bf moonset}. &
  % Moon
  % (keep helping)
  &
  % Recorder
  {\bf New} Moon sets at \ \underline{\hspace{\moontime}}
  \\\hline

  %
  % waxing crescent
  %
  11 &
  % Earth
  %Help the Moon move to the {\bf waxing crescent} Moon.
  &
  % Moon
  Move to the {\bf waxing crescent} Moon. &
  % Recorder 
  % (get ready)
  \\\hline
  12 & 
  % Earth
  Rotate the Earth until {\bf moonrise}. &
  % Moon
  Help find the observer's local time. &
  % Recorder
  {\bf Waxing crescent} Moon rises at \ \underline{\hspace{\moontime}}     
  \\[2ex]
  &
  % Earth
  Rotate the Earth until {\bf moonset}. &
  % Moon
  % (keep helping)
  &
  % Recorder
  {\bf Waxing crescent} Moon sets at \ \underline{\hspace{\moontime}}
  \\\hline  
\end{tabularx}

\clearpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Third set
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\centerline{\Large\it Everyone\ \  switch\ \  jobs}
\bigskip

\begin{tabularx}{\textwidth}{|c|X|X|X|}\hline
  \rowcolor[gray]{0.8}
  &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{{\bf Earth}} &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{{\bf Moon}} & 
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{{\bf Recorder}} \\
  % roles
  \rowcolor[gray]{0.8}
  &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{Partner 2} &
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{Partner 3} & 
  \multicolumn{1}{>{\columncolor[gray]{0.8}}c|}{Partner 1} \\\hline\hline
  13 &
  % Earth
  Hold the Earth straight up-and-down in the ``sunlight''. When you
  rotate the Earth, remember it always rotates to the East. 
  &
  % Moon
  Hold the Moon about an arm's length from Earth and make one slow
  orbit around Earth.  Be sure the NEAR side of the Moon is always facing 
  towards the Earth. 
  &
  % Recorder
  Watch the Moon and help your partner keep the NEAR side facing towards
  the Earth.  Then record the times below.
  \\\hline

  % 
  % waxing gibbous
  %
  14 &
  % Earth
  &
  % Moon
  Move to a {\bf waxing gibbous} Moon.
  &
  % Recorder
  \\\hline
  
  15 &
  % Earth
  Rotate the Earth until {\bf moonrise}.
  &
  % Moon
  Help find the observer's local time.
  &
  % Recorder
  {\bf Waxing gibbous} Moon rises at \ \underline{\hspace{\moontime}}
  \\
  & & & \\
  &
  % Earth
  Rotate the Earth until {\bf moonset}.  &
  % Moon
  % (continue helping)
  &
  % Recorder
  {\bf Waxing gibbous} Moon sets at \ \underline{\hspace{\moontime}}
  \\\hline
  
  %
  % waning gibbous
  %
  16 &
  % Earth
  %Help the Moon move to {\bf new} Moon.
  &
  % Moon
  Move to a {\bf waning gibbous} Moon. &
  % Recorder 
  % (get ready)
  \\\hline
  17 & 
  % Earth
  Rotate the Earth until {\bf moonrise}. &
  % Moon
  Help find the observer's local time. &
  % Recorder
  {\bf Waning gibbous} Moon rises at \ \underline{\hspace{\moontime}}     
  \\[4ex]
  &
  % Earth
  Rotate the Earth until {\bf moonset}. &
  % Moon
  % (keep helping)
  &
  % Recorder
  {\bf Waning gibbous} Moon sets at \ \underline{\hspace{\moontime}}
  \\\hline

  %
  % waning crescent
  %
  18 &
  % Earth
  %Help the Moon move to the {\bf waxing crescent} Moon.
  &
  % Moon
  Move to the {\bf waning crescent} Moon. &
  % Recorder 
  % (get ready)
  \\\hline
  19 & 
  % Earth
  Rotate the Earth until {\bf moonrise}. &
  % Moon
  Help find the observer's local time. &
  % Recorder
  {\bf Waning crescent} Moon rises at \ \underline{\hspace{\moontime}}     
  \\[4ex]
  &
  % Earth
  Rotate the Earth until {\bf moonset}. &
  % Moon
  % (keep helping)
  &
  % Recorder
  {\bf Waning crescent} Moon sets at \ \underline{\hspace{\moontime}}
  \\\hline
  
\end{tabularx}


\bigskip
\centerline{\Large\it When you've completed all the Moon phases, ask
  your TA for Part 4: Questions}

%
% Questions
%

\clearpage
\enlargethispage{4ex}

\ \vspace{-8ex}

\renewcommand{\arraystretch}{1.25}
\begin{tabularx}{\textwidth}{@{}rXrp{3cm}rp{3cm}@{}}
  Name & & ID No. & & Tutorial Day/Time &  \\\cline{2-2}\cline{4-4}\cline{6-6}
\end{tabularx}

\bigskip

{\Large Part 4: Questions} \ \ \ Please hand in this worksheet when you are finished.

\begin{enumerate}

\item The calendar on the back of this page shows the phase of the Moon for
  every day of the year.  Find and
  highlight today's date.  What is the phase of the Moon today?
  \phantom{\Huge 8}\hrulefill
  
  Draw a diagram showing the geometry of the
  Sun, Earth and Moon today.


  \vspace{30ex}

  What time is it right now?  \underline{\hspace{4cm}} \ \  Mark your
  location on the Earth in your diagram.
  
  \medskip

  If you go outside right now and the sky is clear, can you see the Moon?
    
  \begin{tabular}{cl}
    \checkbox & You can never see the Moon during the day. \\
    \checkbox & No, the Moon is below the horizon.\\
    \checkbox & Yes, the Moon is up.
    \end{tabular}

\item \begin{tabularx}{0.95\textwidth}[t]{@{}Xr@{}}
  Let's assume that any time between moonrise and moonset, the Moon
  is visible. In other words, we won't worry about buildings, trees or clouds
  that block our view.

  \medskip
  
  In Part~3 of the tutorial, you found the times when a certain Moon
  phase is visible. In this question, you find the phases visible at a
  certain time of day.  For each phase of the Moon in this 
  list, check ``Yes'' if the Moon is {\bf visible at 1 a.m.} or
  ``No'' if it's not.

  &
  \renewcommand{\arraystretch}{1.25}
  \begin{tabular}[t]{l|cc}
    Phase of & \multicolumn{2}{c}{Moon visible at 1 a.m.?} \\[-0.7ex]
    the Moon & \makebox[2cm]{Yes} & \makebox[2cm]{No} \\\hline
    % phases
    new Moon & \checkbox & \checkbox \\
    waxing crescent & \checkbox & \checkbox \\
    first quarter  & \checkbox & \checkbox \\
    waxing gibbous & \checkbox & \checkbox \\
    full Moon & \checkbox & \checkbox \\
    waning gibbous & \checkbox & \checkbox \\
    third quarter & \checkbox & \checkbox \\
    waning crescent & \checkbox & \checkbox \\
  \end{tabular}
\end{tabularx}

\item You and your friends want to paint stars on the big
  Engineering~{\em E} on the Main Mall.  You're planning on doing it
  next month at 1 a.m.~on a night with {\bf no moonlight}.  Circle the dates
  on the calendar on the back of this page that are good for your evil
  plan.  Which do you think is the best? Explain your reasoning.

  \vfill

\item Look back at the geometry of the full Moon, when the Sun, Earth
  and Moon are lined up. A ``lunar eclipse'' occurs when the Moon passes
  through the Earth's shadow. Why don't we have a lunar eclipse every
  month?

  \vfill


\end{enumerate}

\clearpage
\thispagestyle{empty}
\enlargethispage{1in}

\begin{center}
  \includegraphics[height=9.5in]{MoonPhases2011_lcal}\\
  Downloaded from \url{http://pcal.sourceforge.net/}
  %\rput[l](0,1em){\includegraphics[width=10in]{MoonPhases2011_lcal}}
  % key
  %\rput[l]{R}(2.5in,0in){%
  %  \begin{tabular}{rl}
  %    \pscircle[fillstyle=solid,fillcolor=black](-1mm,1ex){2.5mm} & new Moon \\[1ex]
  %    \pscircle[linewidth=0.5pt](-1mm,1ex){2.5mm} & full Moon 
  %  \end{tabular}}
\end{center}


\end{document}
