In the second half of this morning's activities with the 3-4 graders, we discovered some things about light and telescopes. I handed out diffraction gratings and we looked at the spectrum of the Sun and of the fluorescent lights in the room, discovering that white light is actually composed of many colors. We also looked at discharge tubes filled with different elements, with mercury and helium being the stars. We found that each element emits a unique "fingerprint" of spectral lines. To see a great 2-minute video of everything the kids saw, check this out. This is how we know what stars and other planets are made of.
We then discussed how the colors always appear in a certain order in a rainbow or a diffraction grating: red, orange, yellow, green, blue, violet. Could there be any light which appears before red? Yes, it's called infrared, and we can build cameras to see it even though our eyes can't. I showed this nice video demonstrating the properties of infrared light. Could there be any light which appears after violet? Yes, ultraviolet, and after that would be X-rays and finally gamma rays. We talked about X-rays for a while because some kids were worried about it being dangerous. (Like many other things, they are safe if used properly, but dangerous if not. A yearly dental X-ray is ok, but how do we protect the parts of our bodies which don't need to be X-rayed? And how do we protect the workers who administer dozens of X-rays each day?) I extended that discussion to the ultraviolet and sunlight.
All this was a springboard for discussing telescopes, which is one of the last astronomy standards I hadn't covered yet. Specialized telescopes are built to look at all kinds of light, from gamma rays to the infrared and radio. I showed pictures of some of the big telescopes I have used in my research, and that led to all kinds of interesting questions. We ran out of time, so I may start next Friday by answering more telescope questions.
Friday, May 31, 2013
Scale Model Solar System Complete!
This morning I guided the 3-4 graders through assembling our scale model solar system. I wanted them to really think about how to make a scale model, so I returned to each student the graph they had made last time and I asked them to use the graph to figure out where they would put their planet, given that I had put Teacher Moné's beautiful Earth poster 2.5 meters from the Sun poster. Of course, I found that I needed to break this task into smaller chunks for them to process. We began by revisiting some of the steps we had done last week. Each child identified his/her planet on the graph, read its distance off the graph, and then we thought about what that distance means. For example, Jupiter is at a distance of 5 on the graph. Five what? The graph doesn't say. But the graph itself is a scale model of the solar system. We don't really care what the actual distance is because we are simply stretching this scale model to become a larger scale model which will fill the school. All we need to do is choose a reference point and stretch everything else accordingly. The graph made this easy because it shows Earth as being at a distance of 1. So if Jupiter is at 5, we simply need to put Jupiter 5 times farther from the Sun than Earth is from the Sun; in other words 5x2.5 meters or 12.5 meters.
To help the kids visualize this, I took a rubber band and marked three dots on it, representing Sun, Earth, and Jupiter. This is a scale model much like the graph (if we ignore the vertical dimension of the graph). If I stretch the rubber band, will Jupiter still be 5 times more distant from the Sun than the Earth is from the Sun? Some kids said no and some said yes, so we took a vote. Having to commit to a vote made the kids think harder and they voted overwhelmingly yes. After the vote I did stretch the rubber band and I did get a bigger scale model. In principle, if we got a really long rubber band, I could mark all the planets' distances at the scale of the graph and then stretch it out to get a giant scale model as big as the school, and that would tell us where to put each planet poster. But since that's impractical, we do the math instead.
This seems to have been more or less the right level of conceptual challenge and the right level of math for the kids. They found it a bit of a challenge, but a doable one that became satisfying rather than frustrating. After looking over each child's computation, we practiced some metacognition. Alex was concerned that his number didn't make sense given what he knew about the relative positions of the Sun, Earth and Venus. It turned out that he was misinterpreting his number as the Earth-Venus distance, but the point was a really important one: always check that your numerical results make sense! I have had so many students make a mistake punching numbers into a calculator, and get a number that obviously doesn't make sense given a moment's thought, but blithely write down the number as if any number displayed by a calculator must be correct. In this case we wrote out the multiplication rather than use a calculator, but the same principle applies: check that the results actually make sense! This goes not only for numbers that you compute, but also for numbers that other people compute for you.
An especially effective way to double-check your number is to perform some completely different procedure; if you just perform the original procedure again, you may easily make the same mistake again. So I thought of a way we could all check our numbers without recomputing anything. I made a list of the students' results, starting with the closest planet and proceeding outward. If the distance numbers didn't increase steadily, that would be a smoking gun indicating a mistake. And we did find a mistake this way, so it was instructive.
Once we had our final numbers, we split into groups to measure off the distances and attach the posters to the walls. We couldn't quite fit Neptune into the school grounds, and Orcus wasn't even close, but we put them up at the far end with a note saying where they should really be. Even after choosing a scale so large that the orbit of Neptune was just outside the fence, the sizes of the planets are really small, smaller than a grain of sand for most planets. Even Jupiter is only 2.4mm across. Space is really big!
Looking at the finished product, I am really happy we did it and spent enough time on it to do it right. We certainly appreciate the solar system much better now, but we also learned new ways of thinking.
To help the kids visualize this, I took a rubber band and marked three dots on it, representing Sun, Earth, and Jupiter. This is a scale model much like the graph (if we ignore the vertical dimension of the graph). If I stretch the rubber band, will Jupiter still be 5 times more distant from the Sun than the Earth is from the Sun? Some kids said no and some said yes, so we took a vote. Having to commit to a vote made the kids think harder and they voted overwhelmingly yes. After the vote I did stretch the rubber band and I did get a bigger scale model. In principle, if we got a really long rubber band, I could mark all the planets' distances at the scale of the graph and then stretch it out to get a giant scale model as big as the school, and that would tell us where to put each planet poster. But since that's impractical, we do the math instead.
This seems to have been more or less the right level of conceptual challenge and the right level of math for the kids. They found it a bit of a challenge, but a doable one that became satisfying rather than frustrating. After looking over each child's computation, we practiced some metacognition. Alex was concerned that his number didn't make sense given what he knew about the relative positions of the Sun, Earth and Venus. It turned out that he was misinterpreting his number as the Earth-Venus distance, but the point was a really important one: always check that your numerical results make sense! I have had so many students make a mistake punching numbers into a calculator, and get a number that obviously doesn't make sense given a moment's thought, but blithely write down the number as if any number displayed by a calculator must be correct. In this case we wrote out the multiplication rather than use a calculator, but the same principle applies: check that the results actually make sense! This goes not only for numbers that you compute, but also for numbers that other people compute for you.
An especially effective way to double-check your number is to perform some completely different procedure; if you just perform the original procedure again, you may easily make the same mistake again. So I thought of a way we could all check our numbers without recomputing anything. I made a list of the students' results, starting with the closest planet and proceeding outward. If the distance numbers didn't increase steadily, that would be a smoking gun indicating a mistake. And we did find a mistake this way, so it was instructive.
Once we had our final numbers, we split into groups to measure off the distances and attach the posters to the walls. We couldn't quite fit Neptune into the school grounds, and Orcus wasn't even close, but we put them up at the far end with a note saying where they should really be. Even after choosing a scale so large that the orbit of Neptune was just outside the fence, the sizes of the planets are really small, smaller than a grain of sand for most planets. Even Jupiter is only 2.4mm across. Space is really big!
Looking at the finished product, I am really happy we did it and spent enough time on it to do it right. We certainly appreciate the solar system much better now, but we also learned new ways of thinking.
Friday, May 24, 2013
Planet Posters
Two weeks ago each student chose a planet (or other solar system object) to research and make a poster about. Today they brought in their posters, and each student told the class what they learned in their research. The kids were very engaged and asked so many good questions that we spent all morning doing this. So next week we will put up the posters at the appropriate distances from the Sun poster (which I made and put up near the school entrance today) to make a scale model of the solar system. The discussions today were so full, frank, and wide-ranging that I can't hope to capture them in a blog post. I will simply leave you with a short video with amazing images of Jupiter's moon Europa.
I think the posters were quite successful as a learning experience. The kids learned by researching and making them, but they also learned by listening to other kids talk about their posters, and they all learned when I answered numerous questions in more depth as they arose. I think a key to real learning is that the posters should not be just a laundry list of facts, but should really be based on the students' questions. When I issued the assignment, I offered some questions they might be interested in answering:
I think the posters were quite successful as a learning experience. The kids learned by researching and making them, but they also learned by listening to other kids talk about their posters, and they all learned when I answered numerous questions in more depth as they arose. I think a key to real learning is that the posters should not be just a laundry list of facts, but should really be based on the students' questions. When I issued the assignment, I offered some questions they might be interested in answering:
- What would it be like to visit? What is the temperature? Is there a solid surface? Would the Sun look bright from that distance? If the temperature is extreme, think about ways to convey how extreme it is.
- Does the planet have moons or rings? If you chose a moon to begin with, briefly describe the host planet.
- What are seasons like on that planet? This depends on how tilted the planet is with respect to its orbit.
- How long is the year on that planet? How long is a day?
- Are there volcanoes? Rocks? Rivers/lakes/oceans? (If so, are they made of water or some other substance? Moons of Jupiter and Saturn are especially interesting in this respect.) Clouds? Earthquakes? Storms? Lightning?
- Could you possibly find life there?
Our Solar System, Graphs, and Classification Schemes
Following the previous week's intro to the solar system, on Friday May 17 I visited the 3-4 grade room and used the solar system as a context for practice with graphs. We used the graphs in turn as a tool for helping us think about how to classify solar system objects. By establishing several clearly different classes of solar system objects, we raised questions about how the solar system might have formed these different classes, and we even began to answer those questions. I think this worked quite well as a coherent activity while asking the students to practice a variety of skills.
The centerpiece was a graph (technically a scatterplot*) of size vs distance from Sun for various solar system objects. My first idea was to help the kids make their own graphs from a table of data, but I discarded that idea as requiring too much time before we got to any science. So I made this graph and handed out a copy to each student:
I still wanted students to graph some data, so I planned to make them analyze and understand this graph as a gateway to getting them to add more points and do more analysis. I think this plan went well. I started with the question: can you identify any of the points? This required them to think about the meaning of the axes, and once they understood, they started saying things like "the top one must be Jupiter, because it's the biggest planet" and "the one most to the right must be Neptune because it's most distant from the Sun." Once they grasped that, they were able to label more and more points until we eventually got them all. (The word "eventually" hides a lot of time spent one-on-one with kids, helping them with the reasoning. Eg, Earth and Venus are almost exactly the same size, but Earth is a bit bigger, so which point is Earth? Double-check your conclusion by looking at distance from the Sun. Does it make sense? Etc.)
This was an excellent activity to make them think about the meaning of the graph rather than getting caught up in big numbers which wouldn't mean much to them anyway. (Jupiter is 90,000 miles across? How big is that?) But now let's think about the numbers. The graph says Earth's distance from the Sun is 1. What is that? One foot? One billion miles? The only unit that makes sense is units of "Earth-Sun distance." In other words, the graph makes it easy to read off the relative distances of the planets. It's a scale model. Again, this makes it easy to think about what the solar system is without getting caught up in a bunch of meaningless numbers. We repeated that exercise with the vertical axis.
Then we looked at whether the planets form any distinct groups. The graph makes it clear that there are two groups: small and close to the Sun, vs large and far from the Sun. What other differences might these groups have? It turns out that the large ones are made of different stuff (mostly gas vs rock), so maybe we should really think of two types of planets (gas giants and rocky planets) rather than thinking that all things called "planet" are similar things.
Next, I took them back to the year 1801 when a new planet was discovered: Ceres. I gave them the Ceres-Sun distance in units of the Earth-Sun distance (2.77) and Ceres' size in Earth-size units (0.07) and asked them to put Ceres on the graph. For the faster students, I gave them three more planets which were discovered soon after Ceres (Pallas**, Juno, and Vesta, which have similar distances and sizes) while the teachers helped the slower students with the graphing. After graphing these, it's clear that they form a distinct group: a group of very small things between Mars and Jupiter. Today we call these things main-belt asteroids, but when they were discovered they were simply called new planets. It was only after discovering many of them that people began to think that maybe we shouldn't call all new discoveries planets, and especially not these new discoveries which clearly form a separate group. The way we think about things is highly dependent on how much information we have.
This took until the break. After the break, we added Pluto to the graph. When Pluto was discovered, it was immediately called a planet because it was much larger than any asteroid, and there was no other category it could have been assigned to. But it does seem a bit out of place on the graph, being substantially smaller than any of the eight planets we started with, and also breaking the pattern of the larger planets being farther from the Sun. Well, it took 60 years, but eventually astronomers started discovering lots of other things roughly as far from the Sun and roughly the same size. I gave the kids data for these new objects: Eris, Sedna, Quaoar, and Orcus to start with.
Just as with the asteroids, it became clear that things like Pluto form a new category: the Kuiper Belt. This is even more clear when we realize that all these things are made of ices***, which is not like the inner planets or the outer planets. Once this new category was recognized, it became silly to continue calling Pluto a planet, just as in the 1800's it became silly to continue calling Ceres, Pallas, Juno, and Vesta planets. Perhaps Pluto should have been in a category of its own from the start, but there was no available category other than "planet," and why create a new category just for one object? Another illustration that the way we think about things depends on how much information we have.
[A side note: astronomers created the additional category "dwarf planet" to describe a body which, regardless of its location, is large enough that its gravity pulls it into a round shape (but smaller than the eight planets). Thus Pluto is both a Kuiper Belt object and a dwarf planet just as I am both a teacher and a father---they are not exclusive categories. But "Kuiper Belt object" is a much more descriptive term because it implies being made of ice, being a certain distance from the Sun, etc, whereas "dwarf planet" implies only that the size is neither very large nor very small.]
Next, we talked about how the solar system might have formed in order to form these different classes of objects. I showed clips from the Birth of the Earth episode of the series How the Earth Was Made. It has some really nice visualizations, and it is constructed around evidence, which is a key feature missing from most science documentaries. It tells science like the detective story it is. We spent probably half an hour on this, but I won't write much here because it's already a long blog post.
To cap off this intense morning, I brought some liquid nitrogen to demonstrate how cold the outer planets are. I froze a racquetball and shattered it just by trying to bounce it off the floor; I froze a banana and showed how it can be used as a hammer (until it shattered), and I made a balloon shrink and then expand again as I warmed it up. LN2 is always a great hit with the kids. On Pluto summers can be just warm enough to vaporize some nitrogen, but right about now Pluto is in early fall, and it will get so cold that nitrogen will not only liquify, it will freeze.
**I got the idea for some of this activity when I saw that the element palladium was so named because for a long time it was fashionable to name newly discovered elements after recently discovered planets. I was long aware of uranium, neptunium, and plutonium being named this way, but I had never made the connection to cerium and palladium. People really thought that asteroids were planets until enough asteroids were discovered.
***Ices includes ice made of materials other than water, such as methane, ammonia, etc.
The centerpiece was a graph (technically a scatterplot*) of size vs distance from Sun for various solar system objects. My first idea was to help the kids make their own graphs from a table of data, but I discarded that idea as requiring too much time before we got to any science. So I made this graph and handed out a copy to each student:
I still wanted students to graph some data, so I planned to make them analyze and understand this graph as a gateway to getting them to add more points and do more analysis. I think this plan went well. I started with the question: can you identify any of the points? This required them to think about the meaning of the axes, and once they understood, they started saying things like "the top one must be Jupiter, because it's the biggest planet" and "the one most to the right must be Neptune because it's most distant from the Sun." Once they grasped that, they were able to label more and more points until we eventually got them all. (The word "eventually" hides a lot of time spent one-on-one with kids, helping them with the reasoning. Eg, Earth and Venus are almost exactly the same size, but Earth is a bit bigger, so which point is Earth? Double-check your conclusion by looking at distance from the Sun. Does it make sense? Etc.)
This was an excellent activity to make them think about the meaning of the graph rather than getting caught up in big numbers which wouldn't mean much to them anyway. (Jupiter is 90,000 miles across? How big is that?) But now let's think about the numbers. The graph says Earth's distance from the Sun is 1. What is that? One foot? One billion miles? The only unit that makes sense is units of "Earth-Sun distance." In other words, the graph makes it easy to read off the relative distances of the planets. It's a scale model. Again, this makes it easy to think about what the solar system is without getting caught up in a bunch of meaningless numbers. We repeated that exercise with the vertical axis.
Then we looked at whether the planets form any distinct groups. The graph makes it clear that there are two groups: small and close to the Sun, vs large and far from the Sun. What other differences might these groups have? It turns out that the large ones are made of different stuff (mostly gas vs rock), so maybe we should really think of two types of planets (gas giants and rocky planets) rather than thinking that all things called "planet" are similar things.
Next, I took them back to the year 1801 when a new planet was discovered: Ceres. I gave them the Ceres-Sun distance in units of the Earth-Sun distance (2.77) and Ceres' size in Earth-size units (0.07) and asked them to put Ceres on the graph. For the faster students, I gave them three more planets which were discovered soon after Ceres (Pallas**, Juno, and Vesta, which have similar distances and sizes) while the teachers helped the slower students with the graphing. After graphing these, it's clear that they form a distinct group: a group of very small things between Mars and Jupiter. Today we call these things main-belt asteroids, but when they were discovered they were simply called new planets. It was only after discovering many of them that people began to think that maybe we shouldn't call all new discoveries planets, and especially not these new discoveries which clearly form a separate group. The way we think about things is highly dependent on how much information we have.
This took until the break. After the break, we added Pluto to the graph. When Pluto was discovered, it was immediately called a planet because it was much larger than any asteroid, and there was no other category it could have been assigned to. But it does seem a bit out of place on the graph, being substantially smaller than any of the eight planets we started with, and also breaking the pattern of the larger planets being farther from the Sun. Well, it took 60 years, but eventually astronomers started discovering lots of other things roughly as far from the Sun and roughly the same size. I gave the kids data for these new objects: Eris, Sedna, Quaoar, and Orcus to start with.
Just as with the asteroids, it became clear that things like Pluto form a new category: the Kuiper Belt. This is even more clear when we realize that all these things are made of ices***, which is not like the inner planets or the outer planets. Once this new category was recognized, it became silly to continue calling Pluto a planet, just as in the 1800's it became silly to continue calling Ceres, Pallas, Juno, and Vesta planets. Perhaps Pluto should have been in a category of its own from the start, but there was no available category other than "planet," and why create a new category just for one object? Another illustration that the way we think about things depends on how much information we have.
[A side note: astronomers created the additional category "dwarf planet" to describe a body which, regardless of its location, is large enough that its gravity pulls it into a round shape (but smaller than the eight planets). Thus Pluto is both a Kuiper Belt object and a dwarf planet just as I am both a teacher and a father---they are not exclusive categories. But "Kuiper Belt object" is a much more descriptive term because it implies being made of ice, being a certain distance from the Sun, etc, whereas "dwarf planet" implies only that the size is neither very large nor very small.]
Next, we talked about how the solar system might have formed in order to form these different classes of objects. I showed clips from the Birth of the Earth episode of the series How the Earth Was Made. It has some really nice visualizations, and it is constructed around evidence, which is a key feature missing from most science documentaries. It tells science like the detective story it is. We spent probably half an hour on this, but I won't write much here because it's already a long blog post.
To cap off this intense morning, I brought some liquid nitrogen to demonstrate how cold the outer planets are. I froze a racquetball and shattered it just by trying to bounce it off the floor; I froze a banana and showed how it can be used as a hammer (until it shattered), and I made a balloon shrink and then expand again as I warmed it up. LN2 is always a great hit with the kids. On Pluto summers can be just warm enough to vaporize some nitrogen, but right about now Pluto is in early fall, and it will get so cold that nitrogen will not only liquify, it will freeze.
Notes
*Notice that this graph is not a histogram, which seems to be the only type of graph elementary teachers ever work with. I see that kids start working with graphs around second grade if not earlier, so by the time they get to college, they should be highly proficient. But in my college classes that students are typically far from proficient. My guess is that much of the time spent on graphs in school is wasted because students are never introduced to the idea of graphing the relationship between two different abstract quantities, which is absolutely key to data analysis and science.**I got the idea for some of this activity when I saw that the element palladium was so named because for a long time it was fashionable to name newly discovered elements after recently discovered planets. I was long aware of uranium, neptunium, and plutonium being named this way, but I had never made the connection to cerium and palladium. People really thought that asteroids were planets until enough asteroids were discovered.
***Ices includes ice made of materials other than water, such as methane, ammonia, etc.
Friday, May 10, 2013
Solar system
Today we blasted off from our Earth-Moon base and explored the other planets. I started with this image of the terrestrial planets, which accurately depicts their relative sizes but not their distances. I brought in a big yoga ball to represent the Sun and we went in order from the Sun (ie from the left in that image). For each planet I elicited what they already knew or thought they knew about each planet, and then enriched it as best I could. For example, they knew Mercury is hot because it's close to the Sun...but what about the side away from the Sun (ie the night side, which is not always the same side)? It is actually very cold; why would that be? To put it another way, why is the day/night temperature variation on Earth not very extreme? That led to a discussion of atmospheres, which further led to a discussion of cratering, which further led to comparisons between Mercury and our Moon (similar size, both airless and cratered, extreme day/night temperature variation). I won't try to document each planet's discussion here, but 45 minutes flew by. (Here are links to a similar image comparing some asteroids in the asteroid belt, one comparing the gas giant planets (aka Jovian planets) and an image comparing the dwarf planets outside Neptune's orbit.) As we went, I filled in a table of planet sizes (diameters) and distances from the Sun, for later reference. I rounded the numbers quite a bit so kids would more easily see the comparisons. For example, rounding the Sun's diameter to 800,000 miles and Earth's to 8,000 we easily see that the Sun is about 100 times bigger across. This is way easier to understand than listing the exact numbers and doing the exact computation to find that it is 109 times bigger across.
Just before the break, I addressed why Pluto is no longer considered a planet. Short answer: it became clear that Pluto was just one of many smallish iceballs which are very unlike terrestrial planets and also very unlike Jovian planets, so they deserve their own class. When Pluto was the only known example, it didn't occur to anyone to put it in its own class. A nice example of how the way we classify things can change as we get more data.
After the break, we worked on understanding the distances and sizes by building scale models. First, we did the pocket solar system to understand the relative distances. It's quite amazing to see how relatively jam-packed the inner solar system is compared to the outer solar system, yet even in the inner solar system there are many tens of millions of miles between planets.
Next, the sizes. With the 65-cm-diameter yoga ball as the Sun, I pulled balls of various sizes out of my box: softball, baseball, tennis ball, ping-pong ball, etc. Because I had two ping-pong balls, students suggested they could be Earth and Venus, which are nearly the same size. Does this accurately depict how much smaller than the Sun these two planets are? Well, Earth is 100 times smaller than the Sun, so on this scale it should be 0.65 cm across, or 6.5mm (1/4 inch). That's way smaller than a ping-pong ball, so I had to rummage around in my kit, where I found some allspice. Allspice varies in size, but we did find some which were 6mm across. That's right, if the Sun is a yoga ball, Earth is the size of an allspice!
Whenever we do a calculation, we have to double-check it. I held up the yoga ball and the allspice and asked the kids if they thought 100 allspice would fit across the yoga ball. Yes, it looks about right. Out of curiosity, how many would fit in the yoga ball? Some of them guessed 100x100, because the yoga ball is 100x bigger in each of the two dimensions which are easily seen. But the yoga ball is also 100x bigger in the third dimension, so its volume is 100x100x100 or 1,000,000 (a million) times bigger. One million Earths could fit into the volume of the Sun. (The Sun's density is a bit less than Earth's, so the Sun's mass is "only" 318,000 times bigger than Earth's. For older kids, adding density and mass to this whole discussion might make sense.)
OK, so now we have Earth and Venus. What about Jupiter? Using the same reasoning, we found a ball about Jupiter's size (a small whiffleball, not much bigger than a ping-pong ball), and Saturn is just a bit smaller. Uranus and Neptune could be represented by small marbles. Mars could be a small allspice or an average peppercorn, and Mercury could be a mustard seed. Amazing! (If you're a teacher who would like to do this kind of activity, check out the peppercorn Earth website for some supporting materials.)
Finally, if these are the sizes of the planets in our scale model, what are the distances between planets? The Earth-Sun distance is about 100 Sun diameters, so we need 65 meters or about 200 feet. That's about the distance from our classroom to the far side of the playground. Jupiter is 5 times farther, so maybe we could put it at the KFC a block or so away. Pluto is 40 times further than Earth from the Sun, so that would be 8,000 feet or 1.6 miles, the distance from school to home for some of the kids. Imagine...all that space in between would be empty. Even Mercury, closest to the Sun, would be about 80 feet away and the size of a mustard seed!
At the end, I asked the students to choose a favorite planet or moon, learn more about it, and make a poster over the next two weeks. We'll put the posters up all over school at the appropriate distances to make a scale model. At the center of each poster will be a small object size to match the scale model. To fit the scale model into the school, some of them will have to be very small objects, like a grain of sand. Teacher Brittany will work with the students on the math for that, and I'll report back on the scale model in a few weeks.
Just before the break, I addressed why Pluto is no longer considered a planet. Short answer: it became clear that Pluto was just one of many smallish iceballs which are very unlike terrestrial planets and also very unlike Jovian planets, so they deserve their own class. When Pluto was the only known example, it didn't occur to anyone to put it in its own class. A nice example of how the way we classify things can change as we get more data.
After the break, we worked on understanding the distances and sizes by building scale models. First, we did the pocket solar system to understand the relative distances. It's quite amazing to see how relatively jam-packed the inner solar system is compared to the outer solar system, yet even in the inner solar system there are many tens of millions of miles between planets.
Next, the sizes. With the 65-cm-diameter yoga ball as the Sun, I pulled balls of various sizes out of my box: softball, baseball, tennis ball, ping-pong ball, etc. Because I had two ping-pong balls, students suggested they could be Earth and Venus, which are nearly the same size. Does this accurately depict how much smaller than the Sun these two planets are? Well, Earth is 100 times smaller than the Sun, so on this scale it should be 0.65 cm across, or 6.5mm (1/4 inch). That's way smaller than a ping-pong ball, so I had to rummage around in my kit, where I found some allspice. Allspice varies in size, but we did find some which were 6mm across. That's right, if the Sun is a yoga ball, Earth is the size of an allspice!
Whenever we do a calculation, we have to double-check it. I held up the yoga ball and the allspice and asked the kids if they thought 100 allspice would fit across the yoga ball. Yes, it looks about right. Out of curiosity, how many would fit in the yoga ball? Some of them guessed 100x100, because the yoga ball is 100x bigger in each of the two dimensions which are easily seen. But the yoga ball is also 100x bigger in the third dimension, so its volume is 100x100x100 or 1,000,000 (a million) times bigger. One million Earths could fit into the volume of the Sun. (The Sun's density is a bit less than Earth's, so the Sun's mass is "only" 318,000 times bigger than Earth's. For older kids, adding density and mass to this whole discussion might make sense.)
OK, so now we have Earth and Venus. What about Jupiter? Using the same reasoning, we found a ball about Jupiter's size (a small whiffleball, not much bigger than a ping-pong ball), and Saturn is just a bit smaller. Uranus and Neptune could be represented by small marbles. Mars could be a small allspice or an average peppercorn, and Mercury could be a mustard seed. Amazing! (If you're a teacher who would like to do this kind of activity, check out the peppercorn Earth website for some supporting materials.)
Finally, if these are the sizes of the planets in our scale model, what are the distances between planets? The Earth-Sun distance is about 100 Sun diameters, so we need 65 meters or about 200 feet. That's about the distance from our classroom to the far side of the playground. Jupiter is 5 times farther, so maybe we could put it at the KFC a block or so away. Pluto is 40 times further than Earth from the Sun, so that would be 8,000 feet or 1.6 miles, the distance from school to home for some of the kids. Imagine...all that space in between would be empty. Even Mercury, closest to the Sun, would be about 80 feet away and the size of a mustard seed!
At the end, I asked the students to choose a favorite planet or moon, learn more about it, and make a poster over the next two weeks. We'll put the posters up all over school at the appropriate distances to make a scale model. At the center of each poster will be a small object size to match the scale model. To fit the scale model into the school, some of them will have to be very small objects, like a grain of sand. Teacher Brittany will work with the students on the math for that, and I'll report back on the scale model in a few weeks.
Wednesday, May 8, 2013
Earth, Moon, Sun
Last Friday I had my second astronomy session with the 3-4 graders. In the first one, we spent a lot of unplanned time on why we don't feel the Earth moving, and also it had been 3 weeks since my last visit, so I spend the first block of time recapping how we know the Earth rotates and how we know the cause of the seasons, and building on that to analyze the Earth-Sun motion.
Do we go around the Sun or does it go around us? We know that one of these two things is happening, because a given star rises at intervals of 23 hours and 56 minutes, whereas the Sun does at 24-hour intervals. (Maven alert: 24 hours is an average which varies with the seasons, but that's too much detail here.) So each day the Sun gets 4 minutes "behind" the stars and over the course of a year it appears to make a complete circuit around the sky relative to the stars. Ancient people knew this without having accurate clocks; they simply observed that the stars they could see at night (ie when the Sun was below the horizon) shifted slowly throughout the year. We also know (as a boy mentioned last time) that the Sun's apparent size varies slightly throughout the year, thus indicating that our distance from the Sun varies slightly throughout the year. [We happen to be closest to the Sun in January; if this shocks you, read about the cause of the seasons.]
I drew two models on the board: one with the Sun going around us in an ellipse (thus varying the distance) and the other with Earth going around the Sun in an ellipse. What would be the observable differences between these two scenarios? This is a tough question!
Think about sitting in a moving car. The roadside trees appear to rush by, but the distant mountains appear to move very slowly. If the Earth moves, we ought to be able to see an effect like this by comparing nearby and distant stars. I had taped some stars around the room and we had a small circular carpet to orbit around, so we practiced that. You could also do this activity in the schoolyard. This effect is called parallax; if Earth is still, we will not see it. The ancient Greeks thought of this, they looked for parallax and didn't see it, so they leaned toward Earth being still. It turns out that even the nearest stars are so far away that the parallax effect is tiny, and was not measured until modern times. So the ancient Greeks were not at all ignorant; they just didn't have precise enough tools to measure this really small effect.
It turns out that the nearest star is about 250,000 times more distant than the Earth-Sun distance, ie the distance which Earth moves. It's as if your car moved one mile but you were asked to discern the difference in your view of mountains 250,000 miles away (eg, on the Moon). I illustrated this dramatically by asking the kids to drawing a one-inch Earth-Sun model on the board, and then drawing a long line representing the distance to the next star and asking the kids to stop me when they thought I had arrived. Kids (even most adults) have no idea how much 250,000 times is; they ask me to stop after 5 feet or so, but I keep going. When I run out of board, I get a roll of toilet paper and start unrolling it, as a way to illustrate a very long line. I keep going even when they tell me to stop. Then, when I run out of toilet paper, I go to the back room and get a cart full of hundreds of rolls of toilet paper! It is really dramatic and fun. I also wrote out the number of miles to the next nearest star on the board: about 24,000,000,000,000 miles. (Kids and even most adults have little idea what a "trillion" really means.)
Knowing these distances, we can answer a few questions about the nature of the Sun and stars. Lights which are further away appear to be fainter, so if we compensate for the enormous distance of the stars, we find that their intrinsic brightness (aka luminosity) is about the same as the Sun. The Sun is just another star! And we can compute that luminosity in terms of watt, just like a light bulb. The Sun's luminosity turns out to be 400,000,000,000,000,000,000,000,000 watts. It is the ultimate source of nearly all the energy we use on Earth. If it burned fuel like coal or oil to produce its energy, it would rapidly run out of energy. Astronomers were stumped for years on what the source of energy could be, until they discovered nuclear fusion (which we may address in more detail next time).
After the break, we looked at kids' observations of the Moon over the past three weeks, and we figured out what model could explain these observations, using as many different ways as possible: kinesthetic activity, going into a dark room with a blacklight and ping-pong balls so each student could move the "Moon" around his/her own head; and a mechanical model I had borrowed. I really think all these ways (and more) are necessary for most people to really get it. I don't have time to write up this activity now, but if you are interested there are plenty of internet resources to help you understand it. I just want to say that the kids' own observations over the previous three weeks were key to demolishing the misconceptions that the Moon is only visible at night, and/or that the Moon is always visible at night. Finally, I want to leave you with some insanely cool pictures of eclipses.
This one shows the Moon at three different times throughout a lunar eclipse (when Earth's shadow falls on the Moon). The ancient Greeks were able to determine from this that the Moon is about 1/4 the diameter of Earth, or about 2000 miles across. Furthermore, they know that for a 2,000-mile-diameter object to look as small as the Moon looks to us, it would have to be about 240,000 miles away.
Do we go around the Sun or does it go around us? We know that one of these two things is happening, because a given star rises at intervals of 23 hours and 56 minutes, whereas the Sun does at 24-hour intervals. (Maven alert: 24 hours is an average which varies with the seasons, but that's too much detail here.) So each day the Sun gets 4 minutes "behind" the stars and over the course of a year it appears to make a complete circuit around the sky relative to the stars. Ancient people knew this without having accurate clocks; they simply observed that the stars they could see at night (ie when the Sun was below the horizon) shifted slowly throughout the year. We also know (as a boy mentioned last time) that the Sun's apparent size varies slightly throughout the year, thus indicating that our distance from the Sun varies slightly throughout the year. [We happen to be closest to the Sun in January; if this shocks you, read about the cause of the seasons.]
I drew two models on the board: one with the Sun going around us in an ellipse (thus varying the distance) and the other with Earth going around the Sun in an ellipse. What would be the observable differences between these two scenarios? This is a tough question!
Think about sitting in a moving car. The roadside trees appear to rush by, but the distant mountains appear to move very slowly. If the Earth moves, we ought to be able to see an effect like this by comparing nearby and distant stars. I had taped some stars around the room and we had a small circular carpet to orbit around, so we practiced that. You could also do this activity in the schoolyard. This effect is called parallax; if Earth is still, we will not see it. The ancient Greeks thought of this, they looked for parallax and didn't see it, so they leaned toward Earth being still. It turns out that even the nearest stars are so far away that the parallax effect is tiny, and was not measured until modern times. So the ancient Greeks were not at all ignorant; they just didn't have precise enough tools to measure this really small effect.
It turns out that the nearest star is about 250,000 times more distant than the Earth-Sun distance, ie the distance which Earth moves. It's as if your car moved one mile but you were asked to discern the difference in your view of mountains 250,000 miles away (eg, on the Moon). I illustrated this dramatically by asking the kids to drawing a one-inch Earth-Sun model on the board, and then drawing a long line representing the distance to the next star and asking the kids to stop me when they thought I had arrived. Kids (even most adults) have no idea how much 250,000 times is; they ask me to stop after 5 feet or so, but I keep going. When I run out of board, I get a roll of toilet paper and start unrolling it, as a way to illustrate a very long line. I keep going even when they tell me to stop. Then, when I run out of toilet paper, I go to the back room and get a cart full of hundreds of rolls of toilet paper! It is really dramatic and fun. I also wrote out the number of miles to the next nearest star on the board: about 24,000,000,000,000 miles. (Kids and even most adults have little idea what a "trillion" really means.)
Knowing these distances, we can answer a few questions about the nature of the Sun and stars. Lights which are further away appear to be fainter, so if we compensate for the enormous distance of the stars, we find that their intrinsic brightness (aka luminosity) is about the same as the Sun. The Sun is just another star! And we can compute that luminosity in terms of watt, just like a light bulb. The Sun's luminosity turns out to be 400,000,000,000,000,000,000,000,000 watts. It is the ultimate source of nearly all the energy we use on Earth. If it burned fuel like coal or oil to produce its energy, it would rapidly run out of energy. Astronomers were stumped for years on what the source of energy could be, until they discovered nuclear fusion (which we may address in more detail next time).
After the break, we looked at kids' observations of the Moon over the past three weeks, and we figured out what model could explain these observations, using as many different ways as possible: kinesthetic activity, going into a dark room with a blacklight and ping-pong balls so each student could move the "Moon" around his/her own head; and a mechanical model I had borrowed. I really think all these ways (and more) are necessary for most people to really get it. I don't have time to write up this activity now, but if you are interested there are plenty of internet resources to help you understand it. I just want to say that the kids' own observations over the previous three weeks were key to demolishing the misconceptions that the Moon is only visible at night, and/or that the Moon is always visible at night. Finally, I want to leave you with some insanely cool pictures of eclipses.
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| This is a picture of the Moon's shadow falling on Earth during a solar eclipse. |
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