July 16, 2009

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This lesson can be done with students in preparation for the "Magnitude of the Solar System" activity. Students are asked to set up proportions for the scale of the solar system and calculate the sizes of planets and distances in the model.

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This lesson can be done (optionally) prior to the "Magnitude of the Solar System" activity. Before students take a walk of the solar system, they first calculate the sizes and distances for the scale model. In some ways this lesson may appear to let the cat out of the bag, so to speak, by revealing the vastness of the solar system, but, really, until students walk the solar system in the "Magnitude..." lesson, they rarely have a grasp of the scale. In order to complete this lesson students need to be familiar with ratios, proportions, and solving for a single variable.

Any

- Correctly use proportions to calculate an appropriate scale for a model of the solar system
- Apply mathematics to a real-world situation

Why was the Scientific Revolution important and how did it contribute to progress?

Accurate diameters and distances for each planet in the solar system.

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[Note: This activity in its entirety can be found as an attached pdf and doc file]

- Determine the scale to use for a model of the solar system
- Set-up proportions for the diameters and distances of the model
- Calculate the diameters and distances in the model
- Create scaled planets for use in the model

[Sometimes it can be extremely challenging for students to understand the magnitude of the solar system, even with scaled diagrams. In preparation for walking the solar system, I find it helpful for students to calculate the scale for the model we'll be walking so that they understand where the numbers were derived. This activity was modeled after the “Scales of the Universe” exhibit at the Rose Center for Earth and Space, American Museum of Natural History.]

You all have seen the vastness of the universe described, and I imagine that you, like me, can hardly begin to fathom just how large it really is. But what about something smaller, more manageable, like our solar system? How could we go about understanding the size of our solar system?

We see a variety of models of the solar system in pictures, in small plastic models, in the planets in our classroom, and in the scale model spread across Boston. If we were going to create our own model in order to try and tackle this problem, what scale should we use? One of the best places to start may be to consider two of the most important objects in our solar system: Earth and the Sun. We know that the Earth's diameter is 7,953 miles. For simplicity sake, let's just say that the Earth's diameter is roughly 8,000 miles. The Sun's diameter is 864,900 miles. If we were to round the Sun's diameter down to 800,000 miles, then we achieve a fairly simple scale without losing too much accuracy. So far in our scale, Earth is 1/100th the size of the Sun. But, 1/100th of what?

What is a reasonable size for us to work with? [I typically let students talk through a few suggestions. Usually I suggest a scale of 100,000 miles to 1 inch, unless someone else does. This is fairly reasonable for a scale and requires minimal calculations. I have attached the calculations for this model based on this scale. But if a student were to suggest another reasonable scale that the class decided made sense, there's no reason not to calculate based on that scale.]

*Distance:*

First let's tackle distance. For this part of the model, we can calculate each planet's distance from the next working our way out in the solar system from the Sun to Neptune. What would our proportion be for calculating the distance in our model?

Scaled distances of each planet:

Sun to Mercury - 10 yards

Mercury to Venus - 9 yards

Venus to Earth - 7 yards

Earth to Mars - 14 yards

Mars to Jupiter - 95 yards

Jupiter to Saturn - 112 yards

Saturn to Uranus - 249 yards

Uranus to Neptune - 281 yards

Now we need to calculate the diameter of each planet in our scale model. Given that we're using a scale of 100,000 miles to 1 inch, what proportion would we use to calculate the diameter of each planet?

[Once students have correctly figured out the proportion I break them into small groups to determine one planet's diameter in the solar system. When each group shares the diameter they have calculated, students can record all of the data in their individual tables.]Scaled diameter of each planet:

Sun – 8 inches in diameterNow that we have calculated the distance and diameter of the planets in our solar system, what do we do with that information? We make a model, of course!

Mercury – 0.03 inches in diameter

Venus – 0.08 inches in diameter

Earth – 0.08 inches in diameter

Mars – 0.04 inches in diameter

Jupiter – 0.89 inches in diameter

Saturn – 0.75 inches in diameter

Uranus – 0.33 inches in diameter

Neptune – 0.30 inches in diameter

At the end of this lesson I pass out model magic to each group in the color of the planet they calculated the diameter of and that group is responsible for creating the scaled planet. I usually leave five to ten minutes for this so that students can have a brief discussion of how to create the scaled planets. Sometimes they need a reminder that the circumference of a circle is determined by pi*diameter. Students are then responsible for solving the problem of how to create a small sphere with the correct circumference. Students then need to bring their planets to the next lesson so that the walk of the solar system can be set-up.

Calculating the Scale Lesson (pdf)

Calculating the Scale Lesson (doc)

The scale and conversion charts are attached here:

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