\section{Introduction}
When we look up at the night sky we see many different kinds of objects.
Objects you can see with the naked eye are mostly stars and planets,
although in the Southern Hemisphere, two nearby galaxies are visible.
With a small telescope, one can see ``globular clusters'', ``open clusters'',
``gaseous nebulae'' and ``galaxies''.  One very prominent feature which can be
seen without the use of a telescope (in a dark location), is a swath of light 
that sweeps
across the sky in a broad arc, the Milky Way.  We know the Milky Way is
a vast collection of stars that orbit about the center of our Galaxy
in a flattened distribution resembling a plate or disk.  This disk is
often called the Milky Way or the Milky Way disk.  It is but one of the
components that make up our Galaxy.

In this lab, we will try to determine the shape of the Milky Way and
our location in it based on observations of the distribution of several
different types of objects in the sky.

\begin{itemize}
\item{{\it Goals:} to determine the shape of our Galaxy and our place
in it by observing patterns in the distributions of star clusters and
nebulae} 
\item{{\it Materials:} Galaxy map, colored pencils or markers, scissors,
tape, skewer} 
\end{itemize}

\section{Getting used to the ideas}

\label{sect:ideas}

We are trying to determine the shape of our galaxy and our location in
it. Since the Galaxy is so large, we cannot go outside of it and see
what it looks like; instead, we have to infer what it looks like from
our vantage point within the Galaxy.

The situation is even more complicated because, when we look at astronomical
objects from the Earth, we cannot easily distinguish \textit{how far away}
the objects are. We only see in what direction they appear, but two
objects which appear in the same direction are not necessarily at the
same distance.

\subsection{Map Projections}

A hard aspect for some students to grasp is the idea of map projections. If
you have completed the ``Terrestrial Planets'' lab, we discussed the idea of how 
a spherical object (such as the Earth) can be represented on a flat sheet of 
paper.  In Figure \ref{fig:mercator} is a standard map of the Earth called a
``Mercator Projection''. Near the equatorial regions, this type of projection
is not too bad, but as you move to the poles, the projection is terrible!
Antarctica appears to have more land then all of the other continents combined,
but in reality is much smaller than North America. This is because you cannot
perfectly plot a sphere on a rectangular grid.

\begin{figure}[ht]
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{MAPGALAXY/mercator.eps}
\caption{A ``Mercator'' projection of the Earth.}
\label{fig:mercator}
\end{figure}

Map makers have come up with a variety of ways to make better maps that
more correctly represent the actual sizes of objects on a sphere. For example,
the ``Mollweide'' projection seen in Figure \ref{fig:mollweid} uses a 
complex formula to {\it do a better job} at rendering the sizes and shapes
of the Earth's continents, though it also fails really close to the poles.

\begin{figure}[ht]
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{MAPGALAXY/mollweid.eps}
\caption{A ``Mollweide'' projection of the Earth.}
\label{fig:mollweid}
\end{figure}

A clever way to make a map of a globe is to mentally start with a spherical
globe of paper, and then peel off segments of that sphere (like peeling an 
orange) so that we end up with a ragged, but more accurate representation of
the Earth's surface. An example is shown in Figure \ref{fig:polyglobe}. Here it
is slightly more difficult to make out the continents, but we could cut out this 
map with scissors and tape the pieces back together to construct a spherical 
globe!

\begin{figure}[ht]
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{MAPGALAXY/polyglobe.eps}
\caption{A map of the Earth made by ``peeling'' a sphere apart and plotting
the result on a flat sheet of paper.}
\label{fig:polyglobe}
\end{figure}
%Let's start by seeing how we can get an idea about  the distribution of some 
%objects when we can only determine their directions. First we need to
%consider how we might make a map of the directions towards a set of objects.
%Since objects can potentially be seen all around us, including above or
%below is, an appropriate way to map the directions of objects would be to
%put them on a globe. You can imagine that you are standing in the middle
%of the globe and, for every object that you see, you can place it on the
%globe in the direction in which you see it.

%Unfortunately, since a globe is three dimensional, you can't directly
%draw it on a piece of paper. To make a representation of the globe onto
%a piece of paper, we can imagine that we can slice up the globe into
%several segments and paste each one flat onto a piece of paper, like
%this (imagine taking an orange peel and flattening it out):
%
%\begin{figure}[h!]
%\leavevmode
%\epsfxsize=\textwidth
%%\epsfbox{MAPGALAXY/mapfig_1.eps}
%\epsfbox{MAPGALAXY/test.eps}
%\end{figure}

On such a map, objects on the far left are actually very near to objects on
the far right. This is the type of map we will use in this exercise. Sitting
on the Earth's surface, the sky appears to be a spherical entity that surrounds
us--it is like a globe surrounding the globe of the Earth (ask your TA to
show you the ``celestial sphere'' we have in the back room if they haven't
brought it out for you to look at).

To develop your intuition about this sort of map, let's each make a
map of the directions of all of your fellow students. Let's imagine that
we are each standing inside of a globe and you can see all the other 
students in different directions. Let's all agree that ``north'' should
be up towards the ceiling, that the left-most panel in the map is
looking towards the front of the classroom, and that panels to the right
move in a clockwise fashion around the classroom (so the right most panel
is almost all the way back to the front again).  Remember that we are imagining
that you don't know anything about the distance to each student, only
what direction they are seen in.

\begin{figure}[h!]
\leavevmode
\epsfxsize=\textwidth
%\epsfbox{MAPGALAXY/mapfig_1.eps}
\epsfbox{MAPGALAXY/test.eps}
\end{figure}

Now let's compare the maps. How do the maps differ for students in the
middle of the classroom from those of students at the edge of the
classroom?

\clearpage

Now let's imagine we can reconfigure the students so they are distributed 
uniformly throughout the room.  This means there are students above and
below you as well as around you! However, there may be more students in
some directions than in others, depending on where you are located in
the classroom.  Again, make a map of the directions of your fellow students.

\begin{figure}[h!]
\leavevmode
\epsfxsize=\textwidth
%\epsfbox{MAPGALAXY/mapfig_1.eps}
\epsfbox{MAPGALAXY/test.eps}
\end{figure}

Again, let's compare the maps. How do the maps differ for students in the
middle of the classroom from those of students at the edge of the
classroom?

\smallspace

\clearpage

Let's summarize by drawing maps for four different idealized situations:

You are at the center of a uniform distribution of objects.

\begin{figure}[h!]
%\leavevmode
\epsfxsize=\textwidth
%\epsfbox{MAPGALAXY/mapfig_1.eps}
\epsfbox{MAPGALAXY/test.eps}
\end{figure}

You are at the edge of a uniform distribution of objects.

\begin{figure}[h!]
%\leavevmode
\epsfxsize=\textwidth
%\epsfbox{MAPGALAXY/mapfig_1.eps}
\epsfbox{MAPGALAXY/test.eps}
\end{figure}

\clearpage
You are at the center of a flattened distribution of objects.

\begin{figure}[h!]
%\leavevmode
\epsfxsize=\textwidth
%\epsfbox{MAPGALAXY/mapfig_1.eps}
\epsfbox{MAPGALAXY/test.eps}
\end{figure}

You are at the edge of a flattened distribution of objects.

\begin{figure}[h!]
%\leavevmode
\epsfxsize=\textwidth
%\epsfbox{MAPGALAXY/mapfig_1.eps}
\epsfbox{MAPGALAXY/test.eps}
\end{figure}

One final thing to consider for the flattened distribution of objects:
how does the appearance of objects on the map depend on the choice of
where you put the North Pole?

\vskip 1in

\section{The Contents of Our Milky Way Galaxy}

Before we begin this lab, we should briefly introduce (or re-introduce) you
to the various types of objects we will be plotting on our map. The band of
light we call the Milky Way is in fact the sum of the light from billions of
faint, and distant stars. Stars, and objects containing stars, are what we
see with our eye, and those are the types of objects we will be plotting today.
As you have/will find out in your lecture sessions, the Milky Way and other
galaxies like it contain
a number of objects that are not stars (such as molecular gas clouds),
but these do not emit light that the human eye can detect (though we can
infer their presence since they can absorb light!), and we will not be plotting 
those types of objects. Besides the band of light
called the Milky Way, there are four types of objects we will plot today:
Open clusters, Gaseous nebulae, Globular clusters and Galaxies. The first
three of these all belong to our Milky Way galaxy, while galaxies are ``Milky
Ways'' in their own rite, and are located far beyond the boundaries of the
Milky Way.

Depending on which labs your professor has chosen, you might have already
encountered an ``Open'' cluster: the HR Diagram lab deals with the Pleiades,
a well known Open cluster. A picture of the Pleiades is shown in Figure
\ref{fig:pleiades}. The Pleiades consists of about 250 stars that are about
100 million years old. All of the stars in the Milky Way form in clusters.
This is because they condense-out of cold molecular gas that is found in
large clouds. Sometimes the gas cloud is small and produces a handful of stars,
sometimes the gas cloud is large ($>$ 10$^{\rm 6}$ M$_{\rm Sun}$) and produces thousands of stars. Eventually,
however, such a cluster will slowly fall apart, and the stars will wander off
and circle the galaxy with unique orbits (when in a cluster, however, all of
the stars orbit around the galaxy together as a single unit). This is why
astronomers call them ``Open'', they eventually fall apart. If the were 
``Closed'',
they would not fall apart. Why do they fall apart? Because the gravity from
very massive objects (such as molecular clouds) can pull Open clusters apart 
because they have relatively small ($<$ 5,000 M$_{\rm Sun}$) total masses.

\begin{figure}
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{MAPGALAXY/pleiades.eps}
\caption{The Pleiades, an ``Open Cluster'' of relatively young stars.  }
\label{fig:pleiades}
\end{figure}

In contrast, ``Globular clusters'' are ``Closed''. Globular star clusters do
not fall apart. An example is M15 shown in Figure \ref{fig:m15}. Globular
star clusters contain 100,000 stars or more, and thus have large masses,
and the gravity from all of these stars keeps them ``bound'': Even as they
pass by very massive objects, they cannot be pulled apart. Globular clusters
are made up of some of the oldest stars found in our galaxy--in fact, most
astronomers believe that Globular clusters were the first objects that formed
as the large gas cloud that was the ``proto-Milky Way'' collapsed.

\begin{figure}
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{MAPGALAXY/m15.eps}
\caption{M15, a ``Globular Cluster'' which contains about 100,000 very old stars.  }
\label{fig:m15}
\end{figure}

``Gaseous nebulae'' are closely related to Open clusters. When a cluster of
stars first forms, much of the gas left over from the formation of stars is
still present. The hotter stars in the cluster can ``ionize'' this gas
(see the Spectroscopy lab), and cause it to glow. We see this gas as glowing
knots and wisps of material surrounding the stars. The ``Lagoon'' Nebula,
shown in Figure \ref{fig:lagoon}, is where several hundred young stars
are being born. There is a lot of gas and dust that surrounds the very young
open cluster at the center of the Lagoon, and such regions have complex
structures.

\begin{figure}
\centering
\leavevmode
\epsfysize=0.3\textheight
\epsfbox{MAPGALAXY/lagoon.eps}
\caption{The Lagoon nebula, a gaseous nebula that contains several hundred
young stars, some of which are so hot they ionize the hydrogen gas, causing it
to glow.}
\label{fig:lagoon}
\end{figure}

As noted earlier, galaxies are large collections of objects mostly composed of
stars, star clusters, gas, and dust. They are the hosts of Open clusters, 
Globular clusters and Gaseous nebulae (as well as molecular clouds, and some 
other objects we have not mentioned). To see some pretty pictures of galaxies, 
skip ahead to the ``Galaxy Morphology'' lab (the next lab in this manual), where 
images of several different types of galaxies are presented. 

\section{Exercises}

Now we will create maps which show the distribution of different types
of celestial objects in the sky.  In Table \ref{tab:constellations} is
a list of constellations within which bright objects can be observed
using a small telescope.  The list is separated into four sections,
one for each type of object: globular clusters, open cluster, gaseous
nebulae and galaxies.  For each object type we have listed names of
constellations and the number of objects of each type which can be found
within the constellations.

\begin{table}
\caption{Location of different objects in the sky}
\label{tab:constellations}
\begin{tabular}{|l|c|c|c|c|}\hline
\input MAPGALAXY/constellations.tex
\end{tabular}
\end{table}

Figure \ref{fig:constellationsf} has a blank map of the sky with the boundaries
of all the constellations marked on it.  This map is a bit like a map
of the world that shows the borders between countries but nothing else.
Remember however, when we are looking at the sky we are looking up at
the inside of a sphere that completely surrounds us, not down onto the
outside of the Earth.  {\it The continuous band of stars already marked
on the map is the Milky Way.}


For each type of object, your group will construct a separate celestial
sphere.  {\it In the end, you should have four celestial spheres, each
with one type of object marked on it.}

\noindent
{\bf Complete the following steps to construct each sphere:} 

\begin{enumerate}
\item{Mark the location of each object in your set on the celestial
sphere map.  As an approximation, just place the marks near the center of
the constellation the objects are in.  The marks should be dark and large
enough so that you can see the marks on the other side of the sheet.}

\item{Use a different color for each type of object.  This will help you
distinguish the different types of celestial spheres.  (Remember that
each sphere will have only one type of object marked on it.)}

\item{Cut out the map by cutting along the outside bold-face lines.
Be sure {it NOT} to cut off the tabs at the top and bottom of each of
the map sections.  These are essential for the proper construction of
the globes.}

\item{A celestial sphere can be constructed using tape and skewers
(be careful!).  Your TA will give you more detailed instructions.
Be sure that the skewers go through the small circles on the tabs at
the top and bottom of each of the sections of the map.}

\item{Be sure to construct your celestial sphere inside out because the
Earth is really at the center of this ``globe''.  The objects we see
are above and around us so when we construct these spheres, the marks
should be on the inside surface of the sphere.}

\end{enumerate}

Describe the distribution of each type of object.  Work as a group with
each celestial globe and describe the distribution you observe for
each type of object.  Be as detailed as possible and make references to
the plane of the Milky Way which has already been marked on each map
and also the {\it center of the Milky Way Galaxy which is toward the
constellation Sagittarius}.  This information will be used to complete
the questions so make sure you take good notes! {\bf (20 points)}

\noindent
Milky Way: 

\vskip 1in

\noindent
Open Clusters:

\vskip 1in

\noindent
Gaseous Nebulae:

\vskip 1in

\noindent
Globular Clusters:

\vskip 1in

\noindent
Galaxies:

\vskip 1in

\section{Questions}
The following questions are intended to help you reconstruct
the shape of our galaxy based on the exercises done in the lab.
Be sure to answer all parts of the questions and use complete
sentences as always.

\begin{enumerate}
\item Do any of the descriptions of the idealized distributions of objects 
discussed in section \ref{sect:ideas} (i.e. center of flattened distribution,
edge of flattened distribution, center of uniform distribution, edge
of uniform distribution)
match the descriptions of the distributions of the celestial objects?
If so, which ones?  Explain your reasoning. {\bf (10 points)}

\smallspace

\item Considering the answer to the previous question, where do you think
we are located with respect to the system of globular clusters? open clusters?
gaseous nebulae?  Explain your reasoning. {\bf (10 points)}

\smallspace

\item Draw a sketch of the Galaxy based on your answers to Questions
1 and 2.  Draw your picture showing our location relative to the
distributions of the four types of objects.  Be sure to include all four
types of objects and label them. {\bf (15 points)}

\vspace{3.0in}

\item What do you think the distribution of galaxies, as compared with
the distributions of the other objects, tells you about where galaxies
are located? {\bf (10 points)}
\end{enumerate}
\clearpage
\section{Summary (35 points)}  
Please summarize the concepts you learned from this lab.
You might wish to discuss:

\begin{itemize}

\item{Describe each of the 4 types of objects discussed in the lab.}

\item{When you look up into the sky and see a band of stars, what does
that tell you about the structure of the Galaxy you live in?}

\item{Describe the difference (in terms of the 4 objects discussed in
lab) in what you would see if you were {\it a)} standing in the center
of our Galaxy, and {\it b)} standing at the edge of our Galaxy.}

\item{What conclusions can you draw about the distribution of objects
in our galaxy and beyond?} 

\end{itemize}

Use complete sentences, and proofread your summary before handing in
the lab.
\section{Possible Quiz Questions}
\begin{enumerate}
\item What is an open cluster?
\item What is an HII region?
\item What is a map projection?
\item Why are map projections used?
\end{enumerate}

\section{Extra Credit (ask your TA for permission before attempting, 5 points)}
In this lab we have plotted objects that are in the Milky Way galaxy. What 
would the plot look like if we plotted external galaxies? Make sure to research 
this topic so that you have confidence in what you are plotting, and make a 
rough sketch of the distribution of external galaxies (or photocopy one of the 
``orange peel'' diagrams and plot your galaxies on that)

\begin{figure}[p]
\caption{}
\centering
\leavevmode
\epsfysize=1.0\textheight
\epsfbox[-98 -303 712 897]{MAPGALAXY/constellations.eps}
\label{fig:constellationsf}
\end{figure}
%\begin{latexonly}
%\end{latexonly}
%\begin{htmlonly}
%\epsfxsize=0.8\textwidth
%\epsfbox{MAPGALAXY/constellations.ps}
%\end{htmlonly}
%\end{figure}
%llx = -98 lly = -203 urx = 712 ury = 997 
%\end{document}
