\setcounter{figure}{0}
\setcounter{table}{0}
\hspace*{3.0in}Name(s):{\hrulefill} \\
\hspace*{3.25in}Date:{\hrulefill}


\begin{Large}
\section{\bf Phases of the Moon}
\end{Large}

\subsection{Introduction}

Every once in a while, your teacher or TA is confronted by a student with the 
question ``Why can I see the Moon today, is something wrong?''.  Surprisingly,
many students have never noticed that the Moon is visible in the daytime. The 
reason they are surprised is that it confronts their notion that the shadow 
of the Earth is the cause of the phases--it is obvious to them that the Earth
cannot be causing the shadow if the Moon, Sun and Earth are simultaneously
in view! Maybe you have a similar 
idea. You are not alone, surveys of science knowledge show that the idea that 
the shadow of the Earth causes lunar phases is one of the most common 
misconceptions among the general public. Today, you will learn why the Moon 
has phases, the names of these phases, and the time of day when these phases
are visible.\\

Even though they adhered to a ``geocentric'' (Earth-centered) view
of the Universe, it may surprise you to learn that the ancient Greeks 
completely understood why the Moon has phases. In fact, they noticed during 
lunar eclipses (when the Moon {\it does} pass through the Earth's shadow)
that the shadow was curved, and that the Earth, like the Moon, must be
spherical. The notion that Columbus feared he would fall of the edge of
the flat Earth is pure fantasy---it was not a flat Earth that was the
issue of the time, {\it but how big the Earth actually was} that made
Columbus' voyage uncertain.  \\

The phases of the Moon are cyclic, in that they repeat every month. In
fact the word ``month'', is actually an Old English word for the Moon.
That the average month has 30 days is directly related to
the fact that the Moon's phases recur on a 29.5 day cycle. Note that
it only takes the Moon 27.3 days to orbit once around the Earth, but the
changing phases of the Moon are due to the relative to positions of the Sun, 
Earth, and Moon.
Given that the Earth is moving around the Sun, it takes a few days longer
for the Moon to get to the same {\it relative} position each cycle.\\

Your textbook probably has a figure showing the changing phases exhibited
by the Moon each month. Generally, we start our discusion of the changing
phases of the Moon at ``New Moon''. During New Moon, the Moon is invisible
because it is in the same direction as the Sun, and cannot be seen. Note:
because the orbit of the Moon is tilted with respect to the Earth's orbit,
the Moon rarely crosses in front of the Sun during New Moon. When it does,
however, a spectacular ``solar eclipse'' occurs.\\

As the Moon continues in its orbit, it becomes visible in the western sky
after sunset a few days after 
New Moon. At this time it is a thin ``crescent''. With each passing day,
the cresent becomes thicker, and thicker, and is termed a ``waxing'' crescent.
About seven days after New Moon, we reach ``First Quarter'', a phase when
we see a half moon. The visible, illuminated portion of the Moon continues
to grow (``wax'') until fourteen days after New Moon when we reach ``Full 
Moon''. At Full Moon, the entire, visible surface of the Moon is illuminated, 
and we see a full circle. After Full Moon, the illuminated portion of the Moon
declines with each passing day so that at three weeks after New Moon we
again see a half Moon which is termed ``Third'' or ``Last'' Quarter. As the
illuminated area of the Moon is getting smaller each day, we refer to this
half of the Moon's monthly cycle as the ``waning'' portion. Eventually,
the Moon becomes a waning crescent, heading back towards New Moon to begin
the cycle anew.
Between the times of First Quarter and Full Moon, and between Full Moon and 
Third Quarter, we sometimes refer to the Moon as being in a ``gibbous'' phase. 
Gibbous means ``hump-backed''. When the phase is increasing towards Full
Moon, we have a ``waxing gibbous'' Moon, and when it is decreasing, the 
``waning gibbous'' phases.\\

\noindent The objective of this lab is to improve your understanding of the Moon phases [a topic that you WILL see on future exams!].  This concept, the phases of the Moon, involves
\begin{enumerate}
\item the position of the Moon in its orbit around the Earth,
\item the illuminated portion of the Moon that is visible from here in Las Cruces, and
\item the time of day that a given Moon phase is at the highest point in the sky as seen from Las Cruces.
\end{enumerate}

\noindent You will {\bf finish} this lab by demonstrating to your instructor 
that you do clearly understand the concept of Moon phases, including an 
understanding of:

\begin{itemize}
\item which direction the Moon travels around the Earth
\item how the Moon phases progress from day-to-day
\item at what time of the day the Moon is highest in the sky at each phase
\end{itemize}

\noindent {\bf Materials}

\begin{itemize}
\item  small spheres (representing the Moon), with two different colored 
hemispheres.  The {\bf dark} hemisphere represents the portion of the Moon 
not illuminated by the Sun.
\item  flashlight (representing the Sun)
\item  yourself (representing the Earth, and your nose Las Cruces!)
\end{itemize}

\noindent You will use the colored sphere and flashlight as props for this 
demonstration.  Carefully read and thoroughly answer the questions associated 
with each of the five Exercises on the following pages. [Don't be concerned 
about eclipses as you answer the questions in these Exercises]. Using the 
dual-colored sphere to represent the Moon, the flashlight to represent the 
Sun, and a member of the group to represent the Earth (with that person's 
nose representing Las Cruces' location), `walk through' and `rotate through' 
the positions indicated in the Exercise figures to fully understand the 
situation presented.\\
\\
Note that there are additional questions at the end.
\clearpage 
\begin{center}
\begin{large}
{\bf Work in Groups of Three People!}
\end{large}
\end{center}

\subsection{Exercise 1 (10 points)}

The figure below shows a ``top view'' of the Sun, Earth, and eight different positions (1-8) of the Moon during one orbit around the Earth.  Note that the 
distances shown are {\bf not} drawn to scale.\\
\begin{figure}[htb]
\centerline{{\includegraphics[width=10cm]{moonphases_fig1b.jpg}}}
\end{figure}

\noindent {\bf Ranking Instructions:}  Rank (from {\it greatest} to {\it least}) the amount of the Moon's {\bf entire surface} that is illuminated for the eight positions (1-8) shown.\\
\\
{\bf Ranking Order:}  Greatest A \hrulefill B \hrulefill C \hrulefill D \hrulefill E \hrulefill F \hrulefill G \hrulefill H \hrulefill Least\\
\\
{\bf Or}, the amount of the entire surface of the Moon illuminated by sunlight is the same at all the positions. \_\_\_\_\_\_ (indicate with a check mark). \hspace{3in}\\
\\
{\bf Carefully explain} the reasoning for your result:\\
\vspace{2in}

\newpage

\subsection{Exercise 2 (10 points)}

The figure below shows a ``top view'' of the Sun, Earth, and six different positions (1-6) of the Moon during one orbit of the Earth.  Note that the distances shown are {\bf not} drawn to scale.\\
\begin{figure}[htb]
\centerline{{\includegraphics[width=12cm]{moonphases_fig2b.jpg}}}
\end{figure}

\noindent {\bf Ranking Instructions:}  Rank (from {\it greatest} to {\it least}) the amount of the Moon's illuminated surface that is {\bf visible from Earth} for the six positions (1-6) shown.\\
\\
{\bf Ranking Order:}  Greatest A \hrulefill B \hrulefill C \hrulefill D \hrulefill E \hrulefill F \hrulefill Least\\
\\
{\bf Or}, the amount of the Moon's illuminated surface visible from Earth is the same at all the positions. \_\_\_\_\_\_ (indicate with a check mark). \hspace{3in}\\
\\
{\bf Carefully explain} the reasoning for your result:\\
%\vspace{2in}

\newpage

\subsection{Exercise 3 (10 points)}

Shown below are different phases of the Moon as seen by an observer in the Northern Hemisphere.
\begin{figure}[htb]
\centerline{{\includegraphics[width=17cm]{moonphases_fig3b.pdf}}}
\end{figure}

\noindent {\bf Ranking Instructions:}  Beginning with the {\it waxing gibbous} 
phase of the Moon, rank all five Moon phases shown above in the order that the 
observer would see them over the next four weeks (write both the picture
letter and the phase name in the space provided!).\\
\\
{\bf Ranking Order:} \\

\begin{flushleft}
1) \underline{Waxing Gibbous}\\
~ \\
2) \rule{5cm}{0.01cm} \\
~ \\
3) \rule{5cm}{0.01cm} \\
~ \\
4) \rule{5cm}{0.01cm} \\
~ \\
5) \rule{5cm}{0.01cm} \\
~ \\
\end{flushleft}
~ \\
{\bf Or}, all of these phases would be visible at the same time: \rule{1cm}{0.01cm} 
(indicate with a check mark).  \\

\clearpage
%{\bf Carefully explain} your reasoning for ranking this way:\\
%\vspace{2in}
\subsection{Lunar Phases, and When They Are Observable}

The next three exercises involve determining when certain lunar phases 
can be observed. Or, alternatively, determining the approximate time of day 
or night using the position and phase of the Moon in the sky.\\

In Exercises 1 and 2, you learned about the changing geometry of the 
Earth-Moon-Sun
system that is the cause of the phases of the Moon. When the Moon is in
the same direction as the Sun, we call that phase New Moon. During New Moon,
the Moon rises with the Sun, and sets with the Sun. So if the Moon's phase
was New, and the Sun rose at 7 am, the Moon also rose at 7 am--even though
you cannot see it! The opposite occurs at Full Moon: at Full Moon the Moon
is in the opposite direction from the Sun. Therefore, as the Sun sets, the
Full Moon rises, and vice versa. The Sun reaches its highest point in the
sky at noon each day. The Full Moon will reach the highest point in the sky
at midnight. At First and Third quarters, the Moon-Earth-Sun angle is a 
right angle, that is it has an angle of 90$^{\circ}$
(positions 3 and 6, respectively, in the diagram for exercise \#2). At
these phases, the Moon will rise or set at either noon, or midnight (it
will be up to you to figure out which is which!). To help you with
exercises 4 through 6, we include the following figure detailing {\it when
the observed phase is highest} in the sky.\\
~ \\

\begin{figure}[htb]
\centerline{{\includegraphics[width=10cm]{LunarPhaseTimeofDay.jpg}}}
\end{figure}

\clearpage
\subsection{Exercise 4 (6 points)}

In the set of figures below, the Moon is shown in the first quarter phase at different times of the day (or night).  Assume that sunset occurs at 6 p.m. and that sunrise occurs at 6 a.m.\\
\begin{figure}[htb]
\centerline{{\includegraphics[width=15cm]{phases1.jpg}}}
\end{figure}

\noindent {\bf Instructions:}  Determine the time at which each view of the 
Moon would be seen, and write it on each panel of the figure.\\
\vspace{2in}

\newpage

\subsection{Exercise 5 (6 points)}

In the set of figures below, the Moon is shown overhead, at its highest point in the sky, but in different phases.  Assume that sunset occurs at 6 p.m. and that sunrise occurs at 6 a.m.\\
\begin{figure}[htb]
\centerline{{\includegraphics[width=15cm]{phases2.jpg}}}
\end{figure}

\noindent {\bf Instructions:}  Determine the time at which each view of the Moon would have been seen, and write it on each panel of the figure.\\
\vspace{2in}

\newpage

\subsection{Exercise 6 (6 points)}

In the two sets of figures below, the Moon is shown in different parts of the sky and in different phases.  Assume that sunset occurs at 6 p.m. and that sunrise occurs at 6 a.m.\\
\begin{figure}[htb]
\centerline{{\includegraphics[width=15cm]{phases3.jpg}}}
\end{figure}
%\newpage
%\begin{figure}[htb]
%\centerline{{\includegraphics[width=15cm]{phases4.jpg}}}
%\end{figure}

\noindent {\bf Instructions:}  Determine the time at which each view of the Moon would have been seen, and write it on each panel of the figure.\\
\vspace{2in}

\newpage

\subsection{Demonstrating Your Understanding of Lunar Phases}

After you have completed the six Exercises and are comfortable with Moon phases, and how they relate to the Moon's orbital position and the time of day that a particular Moon phase is highest in the sky, you will be verbally quizzed by your instructor ({\it without the Exercises available}) on these topics.  You will use the dual-colored sphere, and the flashlight, and a person representing the Earth to illustrate a specified Moon phase (appearance of the Moon in the sky). You will do this for three different phases. {\bf (17 points)} \\
\vspace{1in}

\newpage
\hspace*{3.0in}Name:{\hrulefill} \\
\hspace*{3.25in}Date:{\hrulefill}\\

\subsection{Take-Home Exercise (35 points total)}

On a separate sheet of paper, answer the following questions:
\begin{enumerate}
\item  If the Earth was one-half as massive as it actually is, how would the time interval (number of days) from one Full Moon to the next in this `small Earth mass' situation compare to the actual time interval of 29.5 days between successive Full Moons?  Assume that all other aspects of the Earth and Moon system, including the Moon's orbital semi-major axis, the Earth's rotation rate, etc. do not change from their current values. ({\bf 15 points})\\

\item What (approximate) phase will the Moon be in one week from today's
lab? ({\bf 5 points})\\

\item  If you were on Earth looking up at a Full Moon at midnight, and you saw an astronaut at the center of the Moon's disk, what phase would the astronaut be seeing the Earth in?  {\bf Draw a diagram to support your answer. (15 points)}
\end{enumerate}

\subsection{Possible Quiz Questions}

\begin{flushleft}
1) What causes the phases of the Moon? \\
2) What does the term ``New Moon'' mean?\\
3) What is the origin of the word ``Month''?\\
4) How long does it take the Moon to go around the Earth once?\\
5) What is the time interval between successive New Moons?\\
\end{flushleft}

\subsection{Extra Credit (make sure you get permission from your
TA before attempting, 5 points)}

Write a one page essay on the term ``Blue Moon''. Describe
what it is, and how it got its name.
\clearpage
~ ~ ~\\
%\vspace{8in}
\mbox{ }

