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\centerline{\bf Astronomy 150 Homework \#1 -- ``The Scale of the Solar System''}
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(This lab was originally developed from a very old tradition in the 
 department of starting off introductory classes with an outdoor demonstration
 of the solar system.  It was formalized by John Collier and Paul Hodge.)

\begin{description}
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\underline{Introduction}

The Solar System is big.  But what does that statement really tell you?
One of the goals of this course is to have each of you develop some sense
for the size of the solar system and the objects in it.  To do that
requires more than just comparing numbers.  It helps to actually design
your own scale model of the solar system and demonstrate it to someone else.

There are other purposes of this exercise.  One is to expose you to some
numbers, like the kinds of numbers we will be using throughout the course
to describe the Solar System.  Astronomy deals mostly with concepts and
ideas, but numbers play a useful role in expressing these ideas.  We want
you to know not only that the Solar System is big, but how big.  Also,
designing and building a scale model will give you a chance to brush up
on your math skills if you haven't used them in a while.  Nothing too
hard, just some manipulations.  This is as complicated as it will get
in the class, and you can expect to run into some math from time to time
when it will help with visualizing or understanding.  The class will be
filled with numbers, not for the sake of making you do algebra, but to
help make comparisons and ideas clearer.

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\item
\underline{Scale Models}

You are all familiar with scale models.  Perhaps you have built models or
played with toy cars or people when you were younger.  Both of these are
examples of scale models.  In the case of model cars, they are usually
1/24th scale.  That means every dimension in the model is 24 times smaller
than the real car.  If the car is 12 feet long, the model car will be
12/24 or 1/2 foot (six inches) long.  The scale factor to convert dimensions
from the real object to the model would be 1/24.

If we asked you to make a scale model of the University District, you might
choose to make one city block equal to one step.  Then the distance in your
model from 40th street to 50th street would be ten steps and the model
might fit inside a typical classroom.  The scale factor in this case is
1 step/1 city block.

The solar system is very large compared to anything you have probably dealt
with before (even though it is tiny compared to the size of our galaxy,
the Milky Way, which is tiny compared to the size of the Universe!) so to
fit the scale model within a realistic volume, like the UW campus, will
require a tiny scale factor.  Luckily, the planets all lie in roughly
the same plane--the solar system is flat--so you don't have to worry about
climbing buildings or renting balloons.

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\underline{The Activity}

Using the data included in the table and the added information that the sun
is a sphere with a radius of about 700,000 km, choose an appropriate scale
factor to describe a scale model of the solar system that you could demonstrate
to your friends.  You should first scale the distances between the Sun and the
planets, then the sizes of the planets, using the distance from the Earth
to the Sun \underline{and} the size of the Sun for reference.  For example,
suppose the Sun were the size of Kane Hall or suppose the distance from the
Earth to the Sun were 1 inch.  What would the scale factor be in each case?
Would these models make useful demonstrations?

It will probably take some trial and error to find a scale factor that will
work for you.  Once you've settled on a scale factor, make a table that
describes your model.  It should start with your scale factor and go from
the Sun to Pluto, the most distant planet.  The table should include both
the distance to the planets and the size of the planets in whatever units
you choose.  The units for the distance and the size do not need to be
the same.  You might want to measure distances in one unit like yards,
meters, steps or inches and the sizes in another unit like tennis balls,
centimeters or gumbals.  Think of something you could use to represent the
Sun and the planets.  Be creative!

By the end of the first class, you should have decided on your strategy
for demonstrating the size of the Solar System, chosen a reasonable scale
factor and started on the table.  During the second class, we will discuss
the models and ask a few of you to demonstrate the scale of the Solar
System to the class.  This may involve going out of the room.

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\underline{What to turn in}

There are two things to turn in at the end of the second class.  First,
a short explanation of how you chose your scale factor to best
demonstrate the scale of the Solar System.  This should be brief.
One paragraph is plenty.  Second, the table that describes your model.

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\underline{What else to do}

Demonstrate your model to someone else, your roommates, friends, parents
or boss.  Can you give them some sense of how spacious space is?

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\centerline{\bf Planets:  Basic Data}
\begin{center}
\begin{tabular}{lc lc lc lc lc lc}
                 & Semi-Major Axis & & Revolution & Diameter & Rotation \\
\underline{Name} & \underline{(10$^6$ km)} & \underline{(AU)} &
\underline{Period} & \underline{(km)} & \underline{(Days)} \\
Mercury & 57.9 & 0.39 & 0.24 yr & 4878 & 58.65 \\
Venus & 108 & 0.72 & 0.62 yr & 12102 & 243.0 (R) \\
Earth & 150 & 1.00 & 1.00 yr & 12756 & 1.00 \\
Mars & 228 & 1.52 & 1.88 yr & 6787 & 1.03 \\
Jupiter & 778 & 5.20 & 11.86 yr & 142984 & 0.41 \\
Saturn & 1426 & 9.54 & 29.46 yr & 120536 & 0.44 \\
Uranus & 2868 & 19.18 & 84.07 yr & 51118 & 0.72 (R) \\
Neptune & 4494 & 30.06 & 164.82 yr & 49660 & 0.70 \\
Pluto & 5900 & 39.44 & 248.6 yr & 2400 & 6.39 (R) \\
\end{tabular}
\end{center}

(R) denotes retrograde rotation.

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