A few years ago I hit upon this project for polar equations of conics. Objects orbiting stars can be modeled more or less as polar ellipses, with their host star as the focus point. With a little Wikipedia finagling, you can recreate our solar system.

It's pretty cool, and with new Desmos labeling abilities, it's easier to distinguish what's what. However, the project had a case of the samsies. Every kid or set of kids was making the same thing. There was a lack of creativity. I don't know why it took me so long, but this year I changed it up. I wrote up an explanatory document and let them design a solar system of their own.

We got some very nice and orderly systems, and some whose planets wouldn't survive very long before ramming each other to pieces. I encouraged creativity with the themes.

This one took a little longer than I thought (about 2 hours or so), but I find it important to relax a bit on time requirements if kids are putting in a lot of effort, and that was definitely the case here. Lots of good discussions about how to vary their objects, what various eccentricities would do, and how to manipulate orbits just so.

AuthorJonathan Claydon