1. Define the NAU or Norbanian Astronomical Unit for your system. Work in groups to do this and divide the tasks. You should have all three planets orbiting the Norbanian sun. Pick one of the planets as your home planet. Measure the distance from the planet's center to the center of the Norbanian sun using a ruler held up to the screen and record it in your notebook. Call that distance one NAU. Next measure the distances from the other planet's centers to the center of the Norbanian sun and record them in your notebook. Now take the ratio of the other planet's distances to the home planet's distance to determine there distances in NAU. Repeat the process with the other planets as your home planet and look at a table of NAUs for each choice of home planet. Once you have all your data, write a short report and a presentation to give before other groups. Each group should give their presentation to all students and all students should discuss the differences and similarities between their results.
2. Does Newton's theory of gravity hold in Norbania? Kepler's Third Law follows from Newton's theory so if it holds, then Newton's theory explains the motion of the planets in Norbania. Kepler's Third Law states that the cube of the radius of the planet's orbit is directly proportional to the square of the planet's period (r3~T2). Whenever one thing is directly proportional to another, the plot of the one thing against the other is a straight line - a very familiar and much used pattern. So if you plot the cube of the radius of the planet's orbit against the square of the planet's period you should get a straight line. You should have three planets so you have as much data as posible to check the straight line behavior. You can measure the planet's radius with a ruler and its period with the clock at the top (just time one complete orbit around the Norbanian sun). Then make a data table and have columns for the cube of the radius of the planet's orbit and square of the planet's period. Then you are ready to plot. Does Kepler's Third Law hold in Norbania? There is a way to check your work. Take the ratio of the radius cubed and the period squared for each planet. It should be the same for all three planets. Compare the two methods.
Before trying challenges 3, 4, or 5, read this section. You can take the activity apart, which is the power of Squeak. Click on the Playing button at the left for a introduction to how Squeak works, if you haven't done this already. You must click Escape Browser and your resolution must be set at 1024x768 to view this properly. Go to Squeakland for tutorials and more information on using Squeak. Again, taking it apart and even breaking it is a good way to learn. No matter how bad a mess you make, you can always get back to the original activity by exiting Squeak and starting over, so don't worry.
3. You can draw your own planet and substitute your drawing for any of the planets in the Planets flap. Open the flap for planet1 (second flap from the top on the right - it's called p1) and grab the script p1script3 (click it once) and drag it out onto the workspace and click once. The script will open up. Next, click on your drawing while holding down the alt key (option key on a Mac). You should see the halo around your drawing. Click on the orange circle in the lower left (if you put your cursor on the orange button balloon help with tell you "Make a tile representing this object"). Grab the tile it made (click once) and drop it onto the end of the script (click to release), which reads Sketch10. Now the planet will look like your drawing. To hide the script, click the brown oval with the O in the center at the upper left of the script window. Now draw your own planet for the other two planets in the Planets flap.
4.Where is Norbert? You saw him in the beginning. Find him and make him do tricks. There is a flap for Norbert on the right at the bottom. To start, open the Norbert flap and explore his scripts. Good luck and have fun.
5. For a super challenge, add another planet to the model. First draw a new planet - that's the easy part. Now you have to figure out how made the planets for the Norbanian system move. You will have to examine my scripts for the colored dots and for the planets by opening their flaps to figure it out. Then just copy what I did for a fourth planet.
HOW IT WORKS: Norbania is designed to follow Kepler's Third Law with circular orbits. It's a good approximation for a massive sun like ours as long as the planets start out in circular orbits. The radius is determined by creating a point with an x value of the difference between the planet's and sun's x values and a y value of the difference between the planet's and sun's y values. The radius is the point's distance (measured from the origin at the lower left). The period is the square root of the radius cubed and this is determined by approximation (see any per's script1). If you don't understand how it works, don't worry, you can still copy what I did for a fourth planet and you will learn something.
6. You may think mathematics and art aren't related, but nothing could be farther from the truth. The sense of beauty you see in art is equally important in mathematics. Symmetry is part of beauty and it runs throughout art and mathematics. Theorems have a sense of beauty because they represent truth. Beauty gives you a sense of balance and well-being in your life. The Squeak project was organized on the page to be functional and that often leads to a kind of beauty. But beauty is in the eye of the beholder, so we challenge you to recreate the Squeak Exercise Challenge project in a way that leaves you with a sense of balance and beauty. With the tools in Squeak, you can make your own drawings. Any of the objects can be moved and resized and their colors can often be changed. Click on any object while holding down the alt key on a PC or the command key on a Mac and you will see the halo of handles. Click on the red handle at the upper left to explore many options for changing the object. Go to Squeakland for tutorials and more information on using Squeak. When you are done go to the NASA CONNECT web site to submit your version of the Squeak project and we will post it to bring beauty and balance into the lives of all who choose to open your project.
