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

\section{Building a Comet}
During this semester we have explored the surfaces of the Moon, terrestrial
planets and other bodies in the solar system, and found that they often are riddled with craters. In Lab 12 there is
a discussion on how these impact craters form. Note that every large body
in the solar system has been bombarded by smaller bodies throughout all of
history. In fact, this is one mechanism by which planets grow in size:
they collect smaller bodies that come close enough to be captured by the
planet's gravity. If a planet or moon has a rocky surface, the surface can
still show the scars of these impact events--even if they occurred many
billions of years ago!  On planets with atmospheres, like our Earth, weather 
can erode these impact craters away, making them difficult to identify. On 
planets that are essentially large balls of gas (the ``Jovian'' planets), 
there is no solid surface to record impacts. Many of the smaller bodies
in the solar system, such as the Moon, the planet Mercury, or the satellites
of the Jovian planets, do not have atmospheres, and hence, faithfully record
the impact history of the solar system. Astronomers have found that when the 
solar system was very young, there were large numbers of small bodies floating 
around the solar system impacting the young planets and their satellites. 
Over time, the number of small bodies in the solar system has decreased. Today 
we will investigate 
how impact craters form, and examine how they appear under different lighting 
conditions.  During this lab we will discuss both asteroids and comets, and 
you will create your own impact craters as well as construct a ``comet''.

\begin{itemize}
\item{{\it Goals:}  to discuss asteroids and comets; create impact craters;
build a comet and test its strength and reaction to light}
\item{{\it Materials:}  A variety of items supplied by your TA}
\end{itemize}

\subsection{Asteroids and Comets}

There are two main types of objects in the solar system that represent
left over material from its formation: asteroids and comets. In fact, both
objects are quite similar, their differences arise from the fact that comets are formed 
from material located in the most distant parts of our solar system, where it 
is very cold, and thus they have large quantities of frozen water and other 
frozen liquids and gases. Asteroids formed closer-in than comets, and are 
denser, being made-up of the same types of 
rocks and minerals as the terrestrial planets (Mercury, Venus, Earth, and 
Mars). Asteroids are generally just large rocks, as shown in Fig. \ref{asteroid}
shown below.\\

\begin{figure}[htpb]
\centerline{{\includegraphics[width=9cm]{Comet/Asteroid460.jpg}}}
\caption{Four large asteroids. Note that these asteroids have craters from
the impacts of even smaller asteroids!}
\label{asteroid}
\end{figure}

The first asteroid, Ceres, was discovered in 1801 by the Italian astronomer
Piazzi. Ceres is the largest of all asteroids, and has a diameter of 933 km
(the Moon has a diameter of 3,476 km).
There are now more than 40,000 asteroids that have been discovered, ranging
in size from Ceres, all the way down to large rocks that are just a few hundred meters across. 
It has been estimated that there are at least 1 million asteroids in the solar 
system with diameters of 1 km or more.  Most 
asteroids are harmless, and spend all of their time in orbits between
those of Mars and Jupiter (the so-called ``asteroid belt'', see
Figure \ref{belt}). Some asteroids,
\begin{figure}[htpb]
\centerline{{\includegraphics[width=6cm]{Comet/asteroidbelt.jpg}}}
\caption{The Asteroid Belt.}
\label{belt}
\end{figure}
however, are in orbits that take them inside that of the Earth, and could 
potentially collide with the Earth, causing a great catastrophe for human life. 
It is now believed that the impact of a large asteroid might have been
the cause for the extinction of the dinosaurs when its collision threw up a 
large cloud of dust that caused the Earth's climate to dramatically cool.
Several searches are underway to insure
that we can identify future ``doomsday'' asteroids so that we have a chance
to prepare for a collision--as the Earth will someday be hit by another
large asteroid.

\subsection{Comets}
Comets represent some of the earliest material left over from the
formation of the solar system, and are therefore of great interest to
planetary astronomers.  They can also be beautiful objects to observe in
the night sky, unlike their darker and less spectacular cousins,
asteroids. They therefore often capture the attention of the public.

\subsection{Composition and Components of a Comet}

Comets are composed of ices (water ice and other kinds of ices),
gases (carbon dioxide, carbon monoxide, hydrogen, hydroxyl,
oxygen, and so on), and dust particles (carbon and silicon).  The dust
particles are smaller than the particles in cigarette smoke.  In
general, the model for a comet's composition is that of a ``dirty
snowball.''
\ref{components}
\begin{figure}[htpb]
\centerline{{\includegraphics[width=6cm]{Comet/partsofcomet.jpg}}}
\caption{The main components of a comet.}
\label{components}
\end{figure}

Comets have several components that vary greatly in composition,
size, and brightness.  These components are the following:
\begin{itemize}
\item{{\it nucleus}: made of ice and rock, roughly 5-10 km across}
\item{{\it coma}: the ``head'' of a comet, a large cloud of gas and dust,
roughly 100,000 km in diameter}
\item{{\it gas tail}: straight and wispy; gas in the coma becomes ionized
by sunlight, and gets carried away by the solar wind to form a
straight blueish ``ion'' tail.  The shape of the gas tail is influenced by
the magnetic field in the solar wind.  Gas tails are pointed in the
direction directly opposite the sun, and can extend 10$^{8}$ km.}
\item{{\it dust tail}: dust is pushed outward by the pressure of sunlight
and forms a long, curving tail that has a much more uniform
appearance than the gas tail.  The dust tail is pointed in the
direction directly opposite the comet's direction of motion, and can
also extend 10$^{8}$ km from the nucleus.}
\end{itemize}

These various components of a comet are shown in the diagram, above (Fig.
\ref{components}).

\subsection{Types of Comets}

Comets originate from two primary locations in the solar system.  One
class of comets, called the {\bf long-period comets}, have long orbits
around the sun with periods of {\it more} than 200 years.  Their orbits are random
in shape and inclination, with long-period comets entering the inner solar 
system from all different directions.  These comets are thought to originate
in the {\bf Oort cloud}, a spherical cloud of icy bodies that extends
from $\sim$20,000 to 150,000 AU from the Sun.  Some of these objects
might experience only one close approach to the Sun and then leave the
solar system (and the Sun's gravitational influence) completely.

In contrast, the
{\bf short-period
comets} have periods less than 200 years, and their orbits are all
roughly in the plane of the solar system.  Comet Halley has a 76-year
period, and therefore is considered a short-period comet.  Comets with
orbital periods $<$ 100 years do not get much beyond Pluto's orbit at
their farthest distance from the Sun.
Short-period comets cannot survive many orbits around the Sun before
their ices are all melted away.  It is thought that these comets
originate in the {\bf Kuiper Belt,} a belt of small icy bodies beyond
the large gas giant planets and in the plane of the solar system.
Quite a few large Kuiper Belt objects have now been discovered, including one
(Eris) that is about the same size as Pluto.
\begin{figure}[htpb]
\centerline{{\includegraphics[width=7cm]{Comet/Oort_cloud.jpg}}}
\caption{The Oort cloud.}
\end{figure}


\begin{figure}[htpb]
\centerline{{\includegraphics[width=7cm]{Comet/kuiper.jpg}}}
\caption{The Kuiper belt.}
\end{figure}

\subsection{The Impacts of Asteroids and Comets}
Objects orbiting the Sun in our solar system do so at a variety of speeds
that directly depends on how far they are from the Sun. For example, the
Earth's orbital velocity is 30 km/s (65,000 mph!). Objects further
from the Sun than the Earth move more slowly, objects closer to the Sun than the
Earth move more quickly. Note that asteroids and comets near the Earth will 
have space velocities similar to the Earth, but in (mostly) random directions,
thus a collision could occur with a relative speed of impact of nearly
60 km/s! How fast is this? Note that the highest muzzle velocity of any
handheld rifle is 1,220 m/s = 1.2 km/s. Thus, the impact of any solar
system body with another is a true {\it high speed collision} that releases a 
large amount of energy. For example, an asteroid
the size of a football field that collides with the Earth with a velocity
of 30 km/s releases
as much energy as one thousand atomic bombs the size of that dropped on
Japan during World War II (the Hiroshima bomb had a ``yield'' of 13 kilotons
of TNT). Since the equation for kinetic energy (the energy of motion) is
K.E. = 1/2(mv$^{\rm 2}$), the energy scales directly as the mass, and mass goes
as the cube of the radius (mass = density $\times$ Volume = density $\times$
R$^{\rm 3}$). A moving object with ten 
times the radius of another traveling at the same velocity has 1,000 times the 
kinetic energy. It is this kinetic energy that is released during a collision.

\subsection{Exercise \#1: Creating Impact Craters}

To create impact craters, we will be dropping steel ball bearings into
a container filled with ordinary baking flour. There are at least two different
sizes of balls, there is one that
is twice as massive as the other. You will drop both of these balls from
three different heights (0.5 meters, 1 meters, and 2 meters), and then measure
the size of the impact crater that they produce. Then on graph paper, you will
 plot the size of the impact crater versus the speed of the impacting ball.

\begin{enumerate}
\item Have one member of your lab group take the meter stick, while another
takes the smaller ball bearing. 
\item Take the plastic tub that is filled with flour, and place it on the floor.
\item Make sure the flour is uniformly level (shake or comb the flour smooth)
\item Carefully hold the meter stick so that it is just touching the top
surface of the flour.
\item The person with the ball bearing now holds the ball bearing so that it
is located exactly one half meter (50 cm) above the surface of the flour.
\item Drop the ball bearing into the center of the flour-filled tub.
\item Use the magnet to carefully extract the ball bearing from the flour so
as to cause the least disturbance.
\item Carefully measure the diameter of the crater caused by this impact, and
place it in the data table, below.
\item Repeat the experiment for heights of 1 meter and 2 meters using the
smaller ball bearing (note that someone with good balance might have to
{\it carefully} stand on a chair to get to a height of two meters!).
\item Now repeat the entire experiment using the larger ball bearing. Record 
all of the data in the data table.\\
\end{enumerate}

\begin{center}
\begin{tabular}{|l|c|c|c|}
\hline
Height & Crater diameter& Crater diameter & Impact velocity \\
 (meters) & (cm) Ball \#1 &(cm) Ball \#2 & (m/s) \\
\hline
0.5 & ~ ~  & ~ ~ & \\
\hline
1.0 & ~ ~  & ~ ~ & \\
\hline
2.0 & ~ ~  & ~ ~ & \\
\hline
\end{tabular}
\end{center}

Now it is time to fill in that last column: Impact velocity (m/s). How
can we determine the impact velocity? The reason the ball falls in the
first place is because of the pull of the Earth's gravity. This force
pulls objects toward the center of the Earth. In the absence of the Earth's
atmosphere, an object dropped from a great height above the Earth's surface
continues to accelerate to higher, and higher velocities as it falls. We
call this the ``acceleration'' of gravity. Just like the accelerator on your
car makes your car go faster the more you push down on it, the force of gravity
accelerates bodies downwards (until they collide with the surface!). 

We will not derive the equation here, but
we can calculate the velocity of a falling body in the Earth's gravitational
field from the equation {\it v} = (2{\it a}y)$^{\rm 1/2}$. In this equation,
``y'' is the height above the Earth's surface (in the case of this lab, it
is 0.5, 1, and 2 meters). The constant ``{\it a}'' is the acceleration of
gravity, and equals 9.80 m/s$^{\rm 2}$. The exponent of 1/2 means that you
take the square root of the quantity inside the parentheses. For example,
if {\it y} = 3 meters, then {\it v} = (2 $\times$ 9.8 $\times$ 3)$^{\rm 1/2}$,
or {\it v} = (58.8)$^{\rm 1/2}$ = 7.7 m/s.\\

1. Now plot the data you have just collected on graph paper. Put the impact
velocity on the {\it x axis}, and the crater diameter on the {\it y} axis. 
({\bf 10 points})

\subsubsection{Impact crater questions}

1. Describe your graph, can the three points for each ball be {\it approximated}
by a single straight line? How do your results for the larger ball compare to that for
the smaller ball?~({\bf 3 points})


\vspace*{3cm}

2. If you could drop both balls from a height of 4 meters, how big would
their craters be? ({\bf 2 points})

\vspace*{2cm}


3. What is happening here? How does the mass/size of the impacting body
effect your results. How does the speed of the impacting body effect
your results? What have you just proven? ({\bf 5 points})

\vspace*{3cm}

\subsection{Crater Illumination}
Now, after your TA has dimmed the room lights, have someone take the
flashlight out and turn it on. If you still have a crater in your tub, great,
if not create one (any height more than 1 meter is fine). Extract the ball
bearing. \\

1. Now, shine the flashlight on the crater from straight over top of
the crater. Describe what you see. ({\bf 2 points})

\vspace*{3cm}

2. Now, hold the flashlight so that it is just barely above the lip of the
tub, so that the light shines at a very oblique angle (like that of the
setting Sun!). Now, what do you see?~({\bf 2 points})


\vspace*{3cm}

3. When is the best time to see fine surface detail on a cratered body, when
it is noon (the Sun is almost straight overhead), or when it is
near ``sunset''? [Confirm this at the observatory sometime this semester!]
({\bf 1 point})

\vspace*{3cm}

\subsection{Exercise \#2: Building a Comet}
In this portion of the lab, you will actually build a comet out of
household materials.  These include water, ammonia, potting soil, and
dry ice (CO$_{2}$ ice).  Be sure to distribute the work evenly among all
members of your group.  Follow these directions: ({\bf 10 points})\\
\begin{enumerate}
\item Use a freezer bag to line the bottom of your bucket.
\item Place a little less than 1 cup of water (this is a little less than 1/2 of
 a ``Solo'' cup!) in the bag/bucket.
\item Add 2 spoonfuls of sand, stirring well.  ({\bf NOTE:} Do not
stir so hard that you rip the freezer bag lining!!)
\item Add a dash of ammonia.
\item Add a dash of organic material (potting soil).  Stir until
well-mixed.
\item  Your TA will place a block or chunk of dry ice inside a towel and crush 
the block with the mallet and give you some crushed dry ice.
\item  Add about 1 cup of crushed dry ice to the bucket, while stirring
vigorously.  ({\bf NOTE:} Do not
stir so hard that you rip the freezer bag!!)
\item  Continue stirring until mixture is almost frozen.
\item  Lift the comet out of the bucket using the plastic liner and shape
it for a few seconds as if you were building a snowball (use gloves!).
\item  Add 1/2 cup water and wait until mixture is frozen.
\item  Unwrap the comet once it is frozen enough to hold its shape.
\end{enumerate}

\subsubsection{Comets and Light}

\begin{enumerate}
\item Observe the comet as it is sitting on a desk.  Make some notes about
its physical characteristics, for example: shape, color, smell ({\bf 5 points}):\\

\vspace*{2 in}

\item Now bring the comet over to the light source (overhead projector) and
place it on top.  Observe, and then describe what happens to the comet
({\bf 5 points}):\\


\vspace*{2 in}

\end{enumerate}

\subsubsection{Comet Strength}

Comets, like all objects in the solar system, are held together by
their internal strength.  If they pass too close to a large body, such
as Jupiter, their internal strength is not large enough to compete
with the powerful gravity of the massive body.  In such encounters, a comet
can be broken apart into smaller pieces.  In 1994, we saw evidence of
this when Comet Shoemaker-Levy/9 impacted into Jupiter.  In 1992,
that comet passed very close to Jupiter and was fragmented into
pieces.  Two years later, more than 21 cometary fragments crashed
into Jupiter's atmosphere, creating spectacular (but temporary) ``scars'' on
Jupiter's cloud deck. \\

\begin{figure}[htpb]
\centerline{{\includegraphics[width=7cm]{Comet/sh-levy.jpg}}}
\caption{The Impact of ``Fragment K" of Comet Shoemaker-Levy/9 with Jupiter. Note
the dark spots where earlier impacts occurred.}
\label{sl9}
\end{figure}

{\bf Exercise:}  After everyone in your group has carefully examined
your comet, it is time to say goodbye.  Take a sample rock and your
comet, go outside, and drop them both on the sidewalk.  What happened
to each object? ({\bf 2 points}) \\

\vspace*{2cm}

\subsubsection{Comet Questions}

\begin{enumerate}

\item  Draw a comet and label all of its components.  Be sure to
indicate the direction the Sun is in, and the comet's direction of motion. 
({\bf 5 points})
\vspace*{4cm}

\item  What are some differences between long-period and short-period
comets?  Does it make sense that they are two distinct classes of
objects?  Why or why not?  ({\bf 5 points})
\vspace*{4cm}

\item  If a comet is far away from the Sun and then it draws nearer as
it orbits the Sun, what would you expect to happen?  ({\bf 5 points})
\vspace*{2cm}

\item  Do you think comets have more
or less internal strength than asteroids, which are composed primarily
of rock?  [Hint: If you are playing outside with your friends in a
snow storm, would you rather be hit with a snowball or a rock?] ({\bf 3 points})\\
\vspace*{4cm}

\end{enumerate}

\clearpage
~ ~ ~\\
\newpage
\subsection{Take Home Exercise (35 points total)}

Write-up a summary of the important ideas covered in this lab. Questions you 
may want to consider are: 

\begin{itemize}
\item{How does the mass of an impacting asteroid or comet affect the size
of an impact crater?}
\item{How does the speed of an impacting asteroid or comet affect the size
of an impact crater?}
\item{Why are comets important to planetary astronomers?}
\item{What can they tell us about the solar system?}
\item{What are some components of comets and how are they affected by the Sun?}  \item{How are comets different from asteroids?}
\end{itemize}

\noindent
Use complete sentences, and proofread your summary before handing it in.

\subsection{Possible Quiz Questions}

\begin{enumerate}
\item What is the main difference between comets and asteroids, and why are
they different?

\item What is the Oort cloud and the Kuiper belt?

\item What happens when a comet or asteroid collides with the Moon?

\item How does weather effect impact features on the Earth?

\item How does the speed of the impacting body effect the energy of the collision?
\end{enumerate}
\subsection{Extra Credit (ask your TA for permission before attempting, 5 points)}

On the 15$^{\rm th}$ of February, 2013, a huge meteorite exploded in the
skies over Chelyabinsk, Russia. Write-up a small report about this event,
including what might have happened if instead of a grazing, or ``shallow'', entry
into our atmosphere, the meteor had plowed straight down to the surface.
\clearpage
~ ~ ~ \\
\newpage
%\end{document}
