\setcounter{figure}{0}
\setcounter{table}{0}
\hspace*{3.0in}Name:{\hrulefill} \\
\hspace*{3.25in}Date:{\hrulefill}
%Comments: i had to manually put in table numbering as I could not
%get it to do it automatically, it was one ahead. need to investigate

\begin{Large}
\section{\bf Scale Model of the Solar System}
\end{Large}

\subsection{Introduction}

The Solar System is large, at least when compared to distances we are familiar 
with on a day-to-day basis.  Consider that for those of you who live here in 
Las Cruces, you travel 2 kilometers (or 1.2 miles) on average to campus each 
day.  If you go to Albuquerque on weekends, you travel about 375 kilometers 
(232.5 miles), and if you travel to Disney Land for Spring Break, you travel 
$\sim$ 1,300 kilometers ($\sim$ 800 miles), where the `$\sim$' symbol means 
``approximately.''  These are all distances we can mentally comprehend.\\
\\
Now, how large is the Earth?  If you wanted to take a 
trip to the center of the Earth (the very hot ``core''), you would travel 6,378 kilometers (3954 miles) from Las 
Cruces down through the Earth to its center.  If you then continued going 
another 6,378 kilometers you would `pop out' on the other side of the Earth in 
the southern part of the Indian Ocean.  Thus, the total distance through the 
Earth, or the {\bf diameter} of the Earth, is 12,756 kilometers ($\sim$ 7,900 
miles), or 10 times the Las Cruces-to-Los Angeles distance. Obviously,
such a trip is impossible--to get to the southern Indian Ocean, you would
need to travel on the surface of the Earth. How far is that? Since the Earth
is a sphere, you would need to travel 20,000 km to go halfway around the
Earth (remember the equation Circumference = 2$\pi$R?). This is a large distance, but 
we'll go farther still.\\
\\
Next, we'll travel to the Moon.  The Moon, Earth's natural satellite, orbits 
the Earth at a distance of $\sim$ 400,000 kilometers ($\sim$ 240,000 miles), or 
about 30 times the diameter of the Earth.  This means that you could 
fit roughly 30 Earths end-to-end between here and the Moon.  This Earth-Moon 
distance is $\sim$ 200,000 times the distance you travel to campus each day (if 
you live in Las Cruces).  So you can see, even though it is located very
close to us, it is a long way to the Earth's nearest neighbor.\\
\\
Now let's travel from the Earth to the Sun.  The {\it average Earth-to-Sun 
distance}, $\sim$ 150 million kilometers ($\sim$ 93 million miles), is referred 
to as one {\bf Astronomical Unit} (AU). When we look at the planets in our Solar 
System, we can see that the planet Mercury, which orbits nearest to the Sun, has
an average distance of 0.4 AU and Pluto, the planet almost always the furthest 
from the Sun, has an average distance of 40 AU. Thus, the Earth's distance from 
the Sun is only 2.5 percent of the distance between the Sun and planet 
Pluto!! Pluto is very far away!\\
\\
The purpose of today's lab is to allow you to develop a better appreciation for 
the distances between the largest objects in our solar system, and the physical
sizes of these objects relative to each other.  To 
achieve this goal, we will use the length of the football field in Aggie 
Memorial Stadium as our platform for developing a scale model of the 
Solar System.  A {\it scale model} is simply a tool whereby we can use 
manageable distances to represent larger distances or sizes (like the road
map of New Mexico used in Lab \#1).  We will properly distribute our planets 
on the football field in the same {\it relative} way they are distributed in 
the real Solar System. {\it The length of the football field will represent the 
distance between the Sun and the planet Pluto}. We will also determine what 
the sizes of our planets should be to appropriately fit on the same scale. 
Before you start, what do you think this model will look like?\\ 

Below you will proceed through a number of steps that will allow for the 
development of a scale model of the Solar System. For this exercise, we will
use the convenient unit of the Earth-Sun distance, the Astronomical Unit (AU).
Using the AU allows us to keep our numbers to manageable sizes.\\

\noindent SUPPLIES: a calculator, Appendix E in your textbook,
the football field in Aggie Memorial Stadium, and a collection of different 
sized spherical-shaped objects\\

\subsection{The Distances of the Planets From the Sun}

Fill in the first and second columns of Table 6.1. In other 
words, list, in 
order of increasing distance from the Sun, the planets in our solar system and 
their average distances from the Sun in Astronomical Units (usually referred to 
as the ``semi-major axis'' of the planet's orbit). You can find these numbers in 
back of your textbook. {\bf (21 points)}\\
\\
\begin{table}[htbp]
\begin{center}
\caption{Planets' average distances from Sun.}
\begin{tabular}{|c|c|c|}\hline
 & \multicolumn{2}{c|}{{\bf Average Distance From Sun}}\\  \cline{2-3}
{\bf Planet} & {\bf ~~~~AU~~~~} & {\bf Yards}\\ \hline \hline
 &  & \\ \hline
 &  & \\ \hline
Earth & 1 & \\ \hline
 &  & \\ \hline
 &  & \\ \hline
 &  & \\ \hline
 &  & \\ \hline
 &  & \\ \hline
Pluto & 40 & 100\\ \hline
\end{tabular}
\label{avedisttab}
\end{center}
\end{table}

\noindent Next, we need to convert the distance in AU into the unit of a football
field: the yard. This is called a ``scale conversion''. Determine the SCALED 
orbital semi-major axes of the planets, based upon the assumption that the 
Sun-to-Pluto average distance in Astronomical Units (which is already entered
into the table, above) is represented by 100 yards, or goal-line to goal-line, 
on the football field. To determine similar scalings for each of the planets, you
must figure out how many yards there are per AU, and use that relationship to
fill in the values in the third column of Table 6.1.

\subsection{Sizes of Planets}

You have just determined where on the football field the planets will be located 
in our scaled model of the Solar System. Now it is time to determine how large 
(or small) the planets themselves are on the {\bf same} scale.\\
\\
We mentioned in the introduction that the diameter of the Earth is 12,756 
kilometers, while the distance from the Sun to Earth (1 AU) is equal to 
150,000,000 km.  We have also determined that in our scale model, 1 AU is 
represented by 2.5 yards (= 90 inches).\\
\\
We will start here by using the largest object in the solar system, the Sun, as 
an example for how we will determine how large the planets will be in our scale 
model of the solar system. The Sun has a diameter of $\sim$ 1,400,000 
(1.4 million) kilometers, more than 100 times greater than the Earth's diameter!
Since in our scaled model 150,000,000 kilometers (1 AU) is equivalent to 2.5
yards, how many inches will correspond to 1,4000,000 kilometers (the Sun's 
actual diameter)? This can be determined by the following calculation:\\
\\
{\bf Scaled Sun Diameter = Sun's true diameter (km) $\times$
\( \frac{(90~in.)}{(150,000,000~km)}\) = 0.84 inches}\\
\\
So, on the scale of our football field Solar System, the {\it scaled Sun} has a 
diameter of only 0.84 inches!! Now that we have established the scaled Sun's 
size, let's proceed through a similar exercise for each of 
the nine planets, and the Moon, using the same formula:\\
\\
{\bf Scaled object diameter (inches) = actual diameter (km) $\times$ \( \frac{(90~in.)}
{(150,000,000~km)} \)}\\
\\
Using this equation, fill in the values in Table 6.2 {\bf (8 points)}.\\

\begin{table}[htbp]
\begin{center}
\caption{Planets' diameters in a football field scale model.}
\begin{tabular}{|c|c|c|}\hline
{\bf Object} & {Actual Diameter (km)} & {\bf Scaled Diameter (inches)}\\ \hline \hline
Sun & $\sim$ 1,400,000 & 0.84\\ \hline
Mercury & 4,878 & \\ \hline
Venus & 12,104 & \\ \hline
Earth & 12,756 & 0.0075\\ \hline
Moon & 3,476 & \\ \hline
Mars & 6,794 & \\ \hline
Jupiter & 142,800 & \\ \hline
Saturn & 120,540 & \\ \hline
Uranus & 51,200 & \\ \hline
Neptune & 49,500 & \\ \hline
Pluto & 2,200 & 0.0013\\ \hline
\end{tabular}
\end{center}
\label{football}
\end{table}

Now we have all the information required to create a scaled model of the Solar 
System. Using any of the items listed in Table 6.3 (spheres of different 
diameter), select the ones that most closely approximate the sizes of your 
scaled planets, along with objects to represent both the Sun and the Moon. \\

\begin{table}[htbp]
\begin{center}
\caption{Objects that Might Be Useful to Represent Solar System Objects}
\begin{tabular}{lc}\hline
{\bf Object} & {\bf Diameter (inches)}\\ \hline
Basketball & 15\\
Tennis ball & 2.5\\
Golf ball & 1.625\\
%White marble & 0.85 \\
Marble & 0.5\\
Peppercorn & 0.08\\
Sesame seed	& 0.07\\
Poppy seed & 0.04 \\
Sugar grain & 0.02\\
Salt grain & 0.01\\
Ground flour & 0.001\\
\hline
\end{tabular}
\end{center}
\label{objects}
\end{table}

Designate one person for each planet, one person for the Sun, and one person 
for the Earth's Moon.  Each person should choose the model object which 
represents their solar system object, and then walk (or run) to that object's 
scaled orbital semi-major axis on the football field.  The Sun will be on the 
goal line of the North end zone (towards the Pan Am Center) and Pluto will be 
on the south goal line.\\

{\bf Observations:}\\

On Earth, we see the Sun as a disk. Even though the Sun is far away,
it is physically so large, we can actually see that it is a round object with
our naked eyes (unlike the planets, where we need a telescope to
see their tiny disks). Let's see what the Sun looks like from the other planets!
Ask each of the ``planets'' whether they can tell that the Sun is a
round object from their ``orbit''. What were their answers? List your results
here: ({\bf 5 points}):\\

\vspace{2.0in}

Note that because you have made a ``scale model'', the results you just found
would be exactly what you would see if you were standing on one of
those planets!\\

\subsection{Questions About the Football Field Model}

\begin{flushleft}
When all of the ``planets'' are in place, note the relative spacing 
between the planets, and the size of the planets relative to these distances.
Answer the following questions using the information you have gained from this 
lab and your own intuition:\\

\vspace{0.25in}

1) Is this spacing and planet size distribution what you expected when you 
first began thinking about this lab today?  Why or why not?  ({\bf 10 points})\\

\vspace{1.75in}

2) Given that there is very little material between the planets (some
dust, and small bits of rock), what do you conclude about the nature
of our solar system? ({\bf 5 points})\\
\vspace{1.50 in}
3)  Which planet would you expect to have the warmest surface temperature?  Why? ({\bf 2 points})\\
\vspace{0.8in}
4)  Which planet would you expect to have the coolest surface temperature?  Why? ({\bf 2 points})\\
\vspace{0.8in}
5)  Which planet would you expect to have the greatest mass?  Why? ({\bf 3 
points})\\
\vspace{0.8in}
%\item  Which planet would you expect to have the greatest density?  Why?
%\vspace{1in}
6)  Which planet would you expect to have the longest orbital period?  Why? ({\bf 2 points})\\
\vspace{0.8in}
7) Which planet would you expect to have the shortest orbital period?  Why?
({\bf 2 points})\\
\vspace{0.8in} 
8) The Sun is a normal sized star. As you will find out at the end
of the semester, it will one day run out of fuel (this will happen in
about 5 billion years). When this occurs, the Sun will undergo dramatic 
changes: it will turn into something called a ``red giant'', a cool star that 
has a radius that may be 100$\times$ that of its current value! When this 
happens, some of the innermost planets in our solar system will be 
``swallowed-up'' by the Sun.  Which ones? ({\bf 5 points}).
\vspace{1.5in}
\end{flushleft}

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

Now you will work out the numbers for a scale model of the Solar System for which the size of New Mexico along Interstate Highway 25 will be the scale.\\
\\
Interstate Highway 25 begins in Las Cruces, just southeast of campus, and 
continues north through Albuquerque, all the way to the border with Colorado. The 
total distance of I-25 in New Mexico is 455 miles. Using this distance to represent 
the Sun to Pluto distance (40 AU), and assuming that the Sun is located at the 
start of I-25 here in Las Cruces and Pluto is located along the Colorado-New Mexico 
border, you will determine:
\begin{itemize}
\item  the scaled locations of each of the planets in the Solar System; that is, you will determine the city along the highway (I-25) each planet will be located nearest to, and how far north or south of this city the planet will be located.  If more than one planet is located within a given city, identify which street or exit the city is nearest to.
\item  the size of the Solar system objects (the Sun, each of the planets) on 
this same scale, for which 455 miles ($\sim$ 730 kilometers) corresponds to 40 
AU.  Determine how large each of these scaled objects will be (probably best to 
use feet; there are 5280 feet per mile), and suggest a real object which well 
represents this size. For example, if one of the scaled Solar System objects 
has a diameter of 1 foot, you might suggest a soccer ball as the object that
best represents the relative size of this object.
\end{itemize}

{\bf If you have questions, this is a good time to ask!!!!!!}\\

\begin{enumerate}
\item  List the planets in our solar system and their average distances from 
the Sun in units of Astronomical Units (AU).  Then, using a scale of 40 AU = 
455 miles (1 AU = 11.375 miles), determine the scaled planet-Sun distances and 
the city near the location of this planet's scaled average distance from the 
Sun.  Insert these values into Table 6.4, and draw on your map of New Mexico 
(on the next page) the locations of the solar system objects. {\bf (20 points)}\\
%[Note: the small black boxes with numbers in them, which are shown along I-25 on the map, are mile markers.]  {\bf [22 points]}\\

\begin{table}[htbp]
\begin{center}
\caption{Planets' average distances from Sun.}
\begin{tabular}{|c|c|c|c|}\hline
 & \multicolumn{2}{c|}{\bf Average Distance from Sun} & \\  \cline{2-3}
{\bf Planet} & {\bf ~~~~in AU~~~~} & {\bf in Miles} & {\bf Nearest City}\\ \hline \hline
 &  & & \\ \hline
 &  & & \\ \hline
Earth & 1 & 11.375 & \\ \hline
 &  & & \\ \hline
Jupiter&5.2 & & \\ \hline
 &  & & \\ \hline
Uranus &19.2& & \\ \hline
 &  & & \\ \hline
Pluto & 40 & 455 & 3 miles north of Raton\\ \hline
\end{tabular}
\end{center}
\label{homework}
\end{table}
\item  Determine the scaled size (diameter) of objects in the Solar System for 
a scale in which 40 AU = 455 miles, or 1 AU = 11.375 miles). Insert these 
values into Table 6.5.  {\bf (15 points)}\\
\\
{\bf Scaled diameter (feet) = actual diameter (km) $\times$ \( \frac{(11.4~mi.~\times~5280~ft/ mile)}{150,000,000~km} \) }\\
\begin{table}[htbp]
\begin{center}
\caption{Planets' diameters in a New Mexico scale model.}
\begin{tabular}{|c|c|c|c|}\hline
{\bf Object} & {\bf Actual Diameter (km)} & {\bf Scaled Diameter (feet)} & {\bf Object}\\ \hline \hline
Sun & $\sim$ 1,400,000 & 561.7 & \\ \hline
Mercury & 4,878 & & \\ \hline
Venus & 12,104 & & \\ \hline
Earth & 12,756 & 5.1 & height of 12 year old\\ \hline
Mars & 6,794 & & \\ \hline
Jupiter & 142,800 & & \\ \hline
Saturn & 120,540 & & \\ \hline
Uranus & 51,200 & & \\ \hline
Neptune & 49,500 & & \\ \hline
Pluto & 2,200 &0.87 &soccer ball \\ \hline
\end{tabular}
\end{center}
\label{newmexico}
\end{table}

\end{enumerate}

\begin{figure}[htbp]
\centerline{{\includegraphics[width=18cm]{ScaleSS/nm_map.jpg}}}
\end{figure}
\clearpage
\subsection{Possible Quiz Questions}

\begin{enumerate}
\item What is the approximate diameter of the Earth? 

\item What is the definition of an Astronomical Unit? 

\item What value is a ``scale model''? 
\end{enumerate}

\subsection{Extra Credit (ask your TA for permission before attempting,
5 points)}
~ \\
Later this semester we will talk about comets, objects that 
reside on the edge of our Solar System. Most comets are found either in 
the ``Kuiper Belt'', or in the ``Oort Cloud''. The Kuiper belt is the region
that starts near Pluto's orbit, and extends to about 100 AU. The Oort cloud,
however, is enormous: it is estimated to be 40,000 AU in radius! Using your
football field scale model answer the following questions:\\
~ \\
1) How many yards away would the edge of the Kuiper belt be from the northern
goal line at Aggie Memorial Stadium?\\
~ \\
2) How many football fields does the radius of the Oort cloud correspond to?
If there are 1760 yards in a mile, how many miles away is the edge of the
Oort cloud from the northern goal line at Aggie Memorial Stadium?\\

\vspace{0.5in}

