Modeling the Solar System
Introduction
The Universe is a pretty big place – 24 billion light years across actually. That means two things. One, it’s too big to visualize. And two, it’s a really big number to work with. But don’t worry; scientists have come up with a solution to these problems. We use models to help us visualize really large (and really small) things. And we use scientific notation to help make really big numbers (as well as really small ones) easier to work with on a regular basis.
Models
Let’s start with models. A scientific model is a simplified view of reality that allows us to create explanations of how we think some part of the world works.
Models may be:
• Physical – i.e. globe
• Spatial – i.e. map
• Mathematical – i.e. D = M/V
• Mental – i.e. A cell is like a city with the nucleus as Town Hall
Different models have different purposes. Some models show structure (i.e. planetarium). Some show process (i.e. orrery). Some give directions (i.e. recipe). Some tell you what something looks like (i.e. globe). No model is going to be effective at everything. But they all help us understand things we cannot touch or see easily.
Many people think, mistakenly, that scientific models are always complicated, impenetrable mathematical equations. And some are. But in truth, many scientific models are just as understandable by kindergarten students as by scientists.
For example, the USDA food pyramid, which recommends the proportions of different kinds of foods in a healthy diet, is a model of the thousands of scientific studies that have been undertaken on the relation among cancer, heart disease and diet. The figure summarizes these studies in a picture that recommends healthy diets. Thus, this figure is a substitute for the many scientific studies on diet, and it is also a substitute for an actual diet.
Models are not just used in science class. In fact, almost every profession relies on models. Here are some examples:
Field / Common type of modelAdvertising / Response to an advertisement tested in a single city is a model of the national response to the ad.
Architecture / The plans for a new building are a model of the actual building.
Business / Past dealings with a client are a model of the trustworthiness and promptness you can expect from her/him in the next deal.
Education / A student's performance on a history exam is a model of everything learned about history since the last exam.
Finance / The rating Morningstar gives a bond fund is a model of the fund's future performance.
Federal gov't / The federal budget is based on an economic model that predicts next year's revenues and expenditures.
Franchising / A company uses its existing stores to model the likely success of stores it is considering building.
Law / A criminal trial provides a model of the actual crime.
Library / The Dewey Decimal System is a model for where books can be found in a library.
Manufacturing / Profit projections are based on a model of material and labor costs as well as sales price.
Medicine / Your doctor's diagnosis of the cause of your back pain is a model of its actual cause.
Prisons / A model, based on age, crime, and family status, is used to predict which prisoners are good candidates for parole.
Retail Sales / The December sales in 1995-2003 model the December sales expected in the coming year.
Theatre / A script is a model of a performance
Your Program Area
Scale
Directly related to a model is Scale – the mathematical relationship between a real-life object and a model of the object. Think about a model airplane. The model is 1/64 the size of the real thing. That’s the scale. And because scale is all about numbers, sometimes these numbers are so big (i.e. model of the universe) or so small (i.e. model of an atom) that we need to use scientific notation when talking about the scale.
Scale can be represented in many ways. Sometimes we just say it:
One inch equals One Thousand Feet
Or
1” = 1000’
Sometimes we use a picture. This is called Graphic Scale.
But far and away, the very best way, is to use a ratio.
1:24,000 which means…
1 unit = 24,000 units, so…
1” = 24,000” (or 2,000 feet)
1’ = 24,000’ (or almost five miles)
1 penny = 24,000 pennies
You will see this type of scale on most maps (often right below the Graphic Scale) and on most physical models. The next time you are building a model airplane (does anybody do that anymore?) or playing with electric trains (does anybody do THAT anymore) or playing with matchbox cars (I know people still do that – but do any ninth graders do that anymore), look on the bottom of the toy and you should see a scale.
In the car shown, the scale is 1:52. So if the toy is 1.5 inches long, how long would the real thing be, in feet? ______
Scientific Notation
Do you know this number, 300,000,000 m/sec.? It's the Speed of light! Do you recognize this number, 0.000,000,000,753 kg? This is the mass of a dust particle! Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on powers of the base number 10.
The number 123,000,000,000 in scientific notation is written as:
The first number 1.23 is called the coefficient and it must be less than 10. The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten.
To write a number in scientific notation:
Put the decimal after the first digit and drop the zeroes.
In the number 123,000,000,000 The coefficient will be 1.23
To find the exponent count the number of places from the decimal to the end of the number.
In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as:
For small numbers we use a similar approach. Numbers less than 1 will have a negative exponent. A millionth of a second is:
0.000,001 sec or 1.0 x 10-6
Rewrite the following paragraph using scientific notation.
Mr. Ruschman is 41 years old. He weighs 0.0815 tons and is 1828.80 mm tall. He has approximately 25,000,000,000,000 cells in his body and a little less than 17 hairs on his head.
Putting It All Together: Size and Scale
Peoria and Beyond
After watching the United Streaming Video Size and Scale: Peoria and Beyond, answer the following questions.
1. Why are models used to study the solar system?
2. What structures in the solar system is it possible to model?
3. What processes in the solar system is it possible to model?
4. Is Sheldon Schafer’s model practical for studying the solar system? What are the advantages and disadvantages of his model?
5. What kind of effect does the Sun have on Pluto? Use Schafer’s model to describe just how far Pluto is from the Sun.
Creating a Linear Model of the Solar System
Now it is your turn to construct a model. In order to get a better idea of the distances between planets and the size of each planet, you are going to make a scale model of the solar system.
Procedure
1. Your teacher will provide you with a data table, measuring tools, and a way to construct the model. Complete the data table prior to constructing your model.
2. Pay careful attention to the instructions your teacher gives you.
3. Using your data table, show the relative size and location of each planet, the Sun, the asteroid belt, and the Kuiper Belt.
4. Be sure to make all measurements from the outside of the Sun.
5. If appropriate color and label all objects in your solar system, including distance from the Sun (in AU) and diameter (relative to Earth).
Questions
1. In what ways is this model similar to and different from the Peoria model?
2. Does this model accurately depict distances from the Sun? Explain.
3. Does this model accurately show the relative sizes of the planets? Explain.
4. Does this model accurately depict the size of the planet relative to the distance from the Sun? Explain.
5. What is the purpose of this model? Why is it used? Why do we need this model?
6. The nearest star to Earth is about 274,000 AU away. How would this fit into your model?
7. The Kuiper Belt is believed to be the place where many of the Solar System’s comets originate. One of the most famous comets is Halley’s Comet, which returns to view about every 76 years. It is next due to arrive in the year 2062. Use your model to construct a hypothesis about why the time between comet sightings is so large.
8. Light travels at a speed of 300,000 km/second. Choose three planets and calculate how long it would take to get there at the speed of light. Remember how far it is to the nearest star? Do you still think the solar system is all that big?
9. Based on your distances between planets, how would you describe space in general and the solar system, in particular?