A Sense of Scale

"Space," it says, "is big. Really big. You just won't believe how vastly, hugely, mindbogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space, listen..." -- The Hitchhiker's Guide to the Galaxy, by Douglas Adams

Big day! And this is crazy detailed, so don't feel obligated to read the whole thing unless you love getting a sense of astronomical scale as much as I do!

This morning P asked about the relative sizes of the Earth and the Moon. As it happened, I'd just been reading an interesting idea or two for learning about that, and she was game, so we gave the activities I'd been reading about a try. Using a curriculum activity like this is not a very unschool-y approach, but P was loving every step, so we ran with it.

First, based on the suggestions in this PDF, P got out two same-size balls of play dough. She divided one of them into larger Earth and smaller Moon pieces and adjusted them until the relative sizes looked right to her. We weighed them on the kitchen scale, and found their masses were in a 2:1 ratio (50 and 25 g, as it happened, so P's money math came in handy). Then I told her that gravity on Earth is six times as strong as gravity on the Moon and asked if she wanted to re-estimate. She did, transferring about 5 g of dough from Moon to Earth. We put the estimated models on post-it notes, which P labeled. Then, since the Earth:Moon volume ratio is 50:1, we divided the other ball of play dough into 50 roughly equal parts (a nice estimation task), picked an average-looking one to be the Moon, and rolled the rest up into a big Earth. The Earth:Moon mass ratio is even higher than 50:1, so I asked some questions to find out how P is thinking about density. She has a pretty good handle on weight-for-size -- this former physics teacher can work with that!

Based on another fun page, we considered that if the Earth were the size of a basketball, the Moon would be tennis-ball sized, and the Sun would be a sphere that could hold the big house across the street with room to spare, but would be much farther away.

Then I asked P how far apart she thought the model Earth and Moon should go compared to their sizes. She remembered from a conversation on another day that if you could roll the Earth like a wheel 10 times, you would cover the distance to the Moon, but it was hard to keep track of complete revolutions of our model. She positioned the models a foot or so apart, and we marked that distance on the table. Then we wrapped a string ten times around the Earth model, stretched it out, and saw that the correct scale distance was more like 4.5 feet -- just a bit longer than our small dining table can hold! I thought P's eyes were going to pop out. She was hooked.

P had been trying to describe how huge the Sun was with numbers like million, billion, and "tillion." I asked if she wanted to see what the numbers really looked like and what they were really called, and she did. So I googled the masses of the Sun and the Earth, wrote them down in scientific notation, and then expanded them to have the appropriate 31 and 25 digits respectively. I showed her hundreds, thousands, millions, billions, trillions, and so on, and then showed her how scientific notation deals with really big numbers with much less writing and fewer names to keep track of. We were working in kilograms, so we used the scale to find something in the kitchen with a mass of 1 kg for reference. A big can of beans with a lump of play dough on top was perfect. I proceeded to model the Earth/Sun size difference with play dough (since the Sun's diameter is about 100 times the Earth's, the Earth was about as small a speck of dough as I could make without getting out a razor blade), and we talked about how people, compared to the Earth, would be much, much smaller than the Earth is compared to the sun. P gleefully came up with bacteria as a possibly appropriate thing to live on our play-dough-speck Earth. Hooray!

More play-dough play ensued. P made some small pancakes and put them next to her Earth model, and I pretended to freak out: "Aaugh! It's a pancake the size of Africa!" and more in that vein. Much hilarity ensued. P made pancakes for several of the continents' sizes, and then she drew a griddle on the paper beneath the pancakes that was bigger than the Earth! ("Help! Help!") She labeled her pancakes pankacs. Rather than correct her, I wrote out three different ways one might spell pancakes, and asked which one looked right to her. We talked about the different ways they could be pronounced, and I noticed P had changed her spelling to panekacs, so I pronounced it. She busted up laughing, and all three of us experimented and laughed about how we could pronounce breakfast tomorrow -- Pan-cakes? Pain-kacks? Pan-kacks? I wondered if T would get confused, but he was totally clear about it, laughing at mistakes and not at the usual pronunciation. I'll bet the correct spelling will be easier for P to come up with next time.

I found myself humming "Somewhere" from West Side Story. P was interested in the music, so I played her several of the less-racist songs from the movie. We talked about the tense race relations depicted in New York between recent Puerto Rican immigrants and the descendants of not-that-much-less-recent immigrants from Europe. I'm trying to make racism an open topic, in light of recent books saying that "colorblindness" doesn't serve the cause of producing less-racist future generations. From the song "America," we talked about how the Puerto Ricans could see a lot to like about living in the U.S., but at the same time could be angry about how abominably they were treated based on their looks and their accents. I don't feel ready to play the Jets' song for P yet -- the racism there is really in your face and even glorified -- but I'm hoping that by laying the groundwork now, I can help her understand the whole movie, and a lot about the big picture of race in the U.S., in time. P and I may see Gnomeo and Juliet for another perspective on love amidst hate and, incidentally, another entry point into Shakespeare.

After the music, we went on a bus-and-walk adventure downtown, running an errand and then playing in a park and visiting the main library. T saw first-hand how bus stops work and asked questions about the PA system on the bus. P saw up close some of the buildings we had seen from far above last Saturday, and she was happy to make the connection. The afternoon was a wonderful, relaxed time, and we took snacks so dinnertime didn't have to be too much of a schedule constraint. We watched someone fishing, saw lots of ducks, and practiced taking turns with another child on an old-fashioned and very fast slide. At the library P saw, and was dying to check out, The Wonderful Wizard of Oz, so now she's stretching her reading level again, without any prodding from me. Life is good.