Great Balls of Fire

After learning about gravity and taking the midmorning break,  the Peregrine 3-4 graders and I worked on understanding nuclear fusion in the core of the Sun and where elements come from.

I started by setting the context.  The students had studied atoms and molecules the previous year so I started by drawing a molecule of water (two hydrogen atoms and one oxygen atom) and reminding them of the evidence for atoms and molecules.  Then we zoomed in to one hydrogen atom and discussed the Rutherford experiment showing that atoms are very fluffy; most of their volume is nearly empty while nearly all their mass is concentrated in a tiny volume in the center (nucleus).  Then we zoomed in further by a factor of 10,000 to the nucleus.  For a hydrogen atom, the nucleus is a single positively charged particle called a proton.  I held up a ping-pong ball as a proton and said that if protons really were that size, the atom would have to be the size of South Davis.

To reinforce the sense of scale, I showed the movie Powers of Ten.  This classic ten-minute movie should be seen by anyone wanting to understand the universe.  I also took the time to answer questions about it.

The basic rules of nuclear physics are actually understandable by anyone. Last year we investigated the effects of electrical charge, and concluded that like charges repel while opposite charges attract. Atoms beyond hydrogen in the periodic table have more protons.  But why do the protons stick together if they repel each other? There must be some form of glue.  I demonstrated two magnets  which repelled each other.  They were "donut" magnets threaded onto a rod so they didn't flop around and the repulsion was clear.  But when I turned the rod vertically and one magnet fell with enough speed onto the other one, they touched briefly.  That was enough for the velcro on their surfaces to attach and keep them together.  The velcro is a short-range force, like the strong nuclear force which keeps a nucleus together.

But protons alone can't generate sufficient strong nuclear force to keep nuclei together.  Another type of particle, with similar mass but no charge and called a neutron, provides the glue.  Nuclei need roughly equal amounts of protons and neutrons to be stable.  I modeled this with a bunch of ping-pong balls I had wrapped with velcro.  The "protons" had velcro hooks and the "neutrons" had velcro loops, so that you needed roughly equal numbers of each to build up a large nucleus.  (The different types were also different colors to make the idea plainly visible.)  Adding a neutron to a nucleus adds mass, but doesn't otherwise change the properties of the atom.  For example, a proton plus a neutron is still hydrogen, but we call it a different isotope of hydrogen.  Similarly, carbon-12 (usually written with a superscript 12 on the left) and carbon-14 are different isotopes of carbon which differ by two neutrons.

With that in mind, we can start building up more complicated elements from hydrogen.  Element number 2 (two protons) is helium, and we need two neutrons to provide the glue so the most common isotope of helium is helium-4.   The protons have to be smashed together at very high speed if they are to ever get close enough for the "velcro" of the strong nuclear force to make them stick, so we need very high temperatures to make this fusion process happen. (High temperature means the individual microscopic particles are wiggling or bounding around at high speed.)  We find it difficult to make these high temperatures on Earth, but the core of the Sun is 15 million degrees (Celsius; tens of millions of degrees if you think in Fahrenheit) and this happens quite routinely.  In fact, most stars turn hydrogen into helium in their cores.

Fusing helium into even heavier elements is harder, but most stars will do that as well by the ends of their lives.   It turns out that crashing two heliums together results in an unstable isotope of element 4 (beryllium), which quickly decays back into two helium-4 nuclei. But if you manage to crash a third helium into the two heliums before the two-helium complex has a chance to decay, you make carbon-12 (the most common isotope of element 6, carbon; again, equal amounts of protons and neutrons).  Then, if you crash another helium into that, you get element number 8: oxygen. Another helium into that produces element 10, argon.  These helium capture reactions are common in massive stars (substantially more massive than the Sun), and they create more of the even-numbered elements than the odd-numbered elements (nitrogen, fluorine, etc).  They go all the way up to iron (element 26).  I modeled all this with the velcro-covered ping-pong balls.

Have you noticed what we've done here?  We've explained the origin of the elements using basic, well-understood physical processes. That's pretty cool! Here's a graph of the observed abundances:

You can see that hydrogen is the most abundant, followed by helium, then the even-numbered elements carbon, oxygen....through iron.  But why are there elements beyond iron if stars only make up to iron? Well, stars make up to iron when they are in equilibrium.  But when they explode (a supernova), so much energy is released that even more complicated nuclei can be made.  I won't explain the details here, but the abundances of all the elements beyond iron are well understood as consequences of supernovae.  That we can understand all the features of the above plot is, to me, one of the most amazing things in all of science.

The supernova explosions are also what throw the newly-manufactured elements back into space, where they can mix into gas clouds that eventually collapse to form new stars. That means that the atoms in your body were once inside another star.  (Not from the Sun, because new atoms made in the Sun won't escape until the end of its life.)

Supernovae make some unstable elements, like uranium.  The most common type of decay for a heavy element is to violently eject a "bullet"  made of two protons and two neutrons, in other words a helium nucleus (again I modeled this with the ping-pong balls).  This is why there is helium on Earth; our gravity is too weak to hold on to helium gas, but helium produced by radioactive decays is trapped in rocks underground.  When we drill for natural gas, we can capture some of this helium and eventually use it to fill balloons.  When it escapes from the balloon, it eventually escapes into space.

Big Bang 

I left out one detail in the story above: most of the helium in the plot was actually made in the Big Bang.  Some of the kids had expressed interest in the Big Bang previously, so I used the remaining time to talk about that.  I used the usual balloon-with-stickers demo, and I also showed this interactive tool made by an undergraduate student of mine. The point of the tool is to show that although we see all galaxies moving away from us, observers in all other galaxies also see all galaxies moving away from them. So we are not at the center of anything. If we think back in time, all galaxies were closer to each other, so the universe was denser (and hotter).  Far enough back in time, the universe was so hot (everywhere) that a fair amount of hydrogen fused into helium.  This is called Big Bang nucleosynthesis (BBN). We can look at the abundance of various  BBN byproducts, like hydrogen-2 (aka deuterium) and confirm that this really happened.

Wrapping up

Most of this trimester we worked on understanding the immense size of space.  If this makes you feel insignificant, remember that you are made of atoms from another star.  You are a part of the universe which can actually understand itself. 

The Gravity of the Situation

Friday was my last day doing astronomy with the 3-4 graders at Peregrine School. The one standard I hadn't yet covered was gravity, so we did gravity before the break (this post) and after the break we discussed nuclear fusion in the Sun's core (next post).

I reviewed some ideas about motion we had discussed last year.  If you roll a marble, you expect it to go in a straight line unless something (another kid, perhaps, or a wall) interferes by pushing (exerting a force) on the marble. That's Newton's first law of motion. I then put a donut on a string and spun the donut in a circle over my head.   What will happen if the string is cut? Will the donut continue in a circle, fly off in a straight line, or fly off in a curve? We took a vote. I always clarify that the question is about what happens immediately, not about what happens eventually, like the donut falling due to the gravity in the room. This means that when we do the experiment, they have to really pay attention!

In reality I don't cut the string, but the string pulls through the soft donut, and it flies off in a straight line---Newton's first law again.  This is a pretty vivid demonstration that the Moon wouldn't keep going  around the Earth, nor the planets around the Sun, unless there was a force keeping them from flying off in a straight line.  Kids this age already know that we call that force gravity, but gravity is also the force that makes things fall when I drop them.  Why do we call these two forces by the same name?

I also have a tennis ball on a string so I can demonstrate circular motion as much as needed.  I do this and ask the kids what direction the force must be in.  It must be towards the center of the circle, where my fist is holding the string.  That's clear because the only direction a string can exert a force is pulling along the string! So whatever force is pulling on the Moon, it must be pointed toward the center of the Earth.  And that's exactly what we observe about gravity on Earth! (It helps to draw an Earth and how the arrow of gravity points in your location vs in, say, Australia.)  So it's quite plausible that these two forces are really the same force.

To bolster the argument that these are the same force, we should look not just at the direction, but also the strength.  I had the kids whirl the tennis ball on a string at various speeds, and feel whether the higher speed requires more force, less force, or the same force (the answer is more).  So let's look at the planets' speeds around the Sun and see if we can relate that to the force of gravity.  I asked the kids for suggestions as to what would affect the planet speed.  The two main suggestions were planet size, and planet distance from the Sun.  It would have been great to investigate both of these possibilities, but we were running short on time so we just did planet distance from the Sun.  I had the kids make graphs of planet speed vs planet distance from the Sun.  We took our time doing this right, figuring out how to draw the axes with reasonable scales, and adding planets one by one, starting with the most familiar ones.

A pattern did emerge: more distant planets are slower, as the graph below shows.

By our tennis ball experiment, slower circular motion implies a weaker pull (less acceleration). Therefore this graph implies that more distant planets feel a weaker pull, and planets closer to the Sun feel a stronger pull.  Does this make sense if the Sun's gravity is what keeps the planets from flying off in straight-line paths?  The kids agreed that it did.

[If we had also made the graph of speed vs planet size, we would not have seen such a clear pattern.  It happens that the outer planets tend to be bigger, so that there would be a tendency for bigger planets to be slower, but it would only be a tendency, not a law, because the biggest planet happens to be the nearest (fastest) of the outer four.  And the pattern would really be broken if we also included Pluto, which is a very distant (hence very slow), small object, providing a counterexample to the fast inner planets which happen to be small and which therefore might give someone the false impression that small means fast.]

I liked this 40-minute activity and I think it worked well.  I did simplify some details to avoid getting bogged down (eg the distinction between force and acceleration), but I think it was appropriate for 3-4 graders who wanted to focus on astronomy rather than physics. We also got in some more practice with graphs, which is important.  And we learned something which in Newton's time was revolutionary: the same laws of physics which we can deduce here on Earth also apply to objects in the sky.   This was one of the most wonderful discoveries in the history of science, and it's what allows us to understand the universe.

Light and Telescopes

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.

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.

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:

• 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? 

I think these questions helped prevent a "laundry list" result.  One thing I would like to do better next time is have some kind of first draft with feedback and then a final draft. I don't know how to do this with posters, but I would like to give kids feedback before it's too late to change the final result.

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.

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.

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.

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 is a picture of the Moon's shadow falling on Earth during a solar eclipse.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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.

Picnic Day

UC Davis Picnic Day is a giant open house attended by 50,000 or more
people. The Physics Club runs a "magic show" and a demo room where
visitors can do some hands-on experiments, but there hasn't been a
kid-friendly physics room in the past.  This year, I decided to make
one with the help of kids and parents at Peregrine School.  The day
before Picnic Day, I brought all my toys (Coriolis effect demo,
balloon in a bottle, infrared camera, mixing colors of light,
airzooka, etc) to the school and spent the morning training students
and parents so they would be able to explain the ideas behind them to
visitors on Picnic Day.  On Friday night my wonderful wife Vera and I
set the demos up in a room on campus, and on Saturday we had a ton of
visitors.

I think we did a really good thing here.  We didn't have our kids
explaining physics to other kids as much as I had imagined, for
various reasons: our kids were having fun playing too; they wanted to
visit other exhibits on Picnic Day; and most of the visitors to our
room were actually adults.  So the kids got less practice in
explaining physics than I had imagined, but we did a great public
service.  As an educator, I'm always thinking about ways to tweak
things, so if there is a next time (or as advice to others thinking
about doing this kind of thing), one way to get kids really deeply
invested might be to have them develop their own unique demos.

There is a season

At the end of last Friday's session with the 3-4 graders we discussed
the seasons. It's natural to think that winter is when we are farther
from the Sun, but is that true?  What evidence can we reason with
here?

Well, for one, we know that when it's winter in the northern
hemisphere, it's summer in the southern hemisphere.  That's a pretty
good clue that the seasons are not caused by the Earth getting closer
to and farther from the Sun.  What else?  One boy, to my amazement,
specifically mentioned that if/when we are closer to the Sun, it
should appear to be bigger, and it doesn't appear to be bigger in
(northern) winter.  I was pretty surprised, but then I recalled that
he had recently seen the movie Agora.  This is a trenchant
observation: the Sun actually looks smallest (as seen from anywhere on
Earth) in January, indicating that January is when Earth is furthest
from the Sun. (You can't see this just by looking, because the Sun is
so blindingly bright and it's a fairly small change, but you can use a
pinhole camera to do it.)


Most people (these kids included) "know" that seasons are caused by
"tilt," but what does that really mean?  It's very useful to take a
globe (on a standard stand tilted by the right amount) and make it
orbit a light source to see how this plays out.  The tilt actually
points to the same place in the sky (judging by the stars) all the
time, but since Earth goes around Sun (or vice versa, it doesn't
matter for this point), for part of the orbit the tilt points the
north pole toward the Sun.  This is northern summer, when there is
midnight Sun near the north pole, and longer daylight hours in
northern latitudes generally.  (You can see this by spinning the globe
in the aforementioned model. Make sure to keep the north pole always
pointing toward the same place in the room, like the clock on the wall,
even as it goes around the "Sun.") Six months later, the Sun is on the
opposite side of Earth (relative to the stars) so it's the south's
turn to have summer and the north pole has constant darkness.  In
between those two extremes, neither hemisphere is favored.

So we are NOT tilted closer to the Sun.  The tilt merely allows the

Sun to shine a greater or lesser fraction of the time on a certain

hemisphere, depending on where the Sun is relative to this constant

tilt.  (This fits the evidence that whatever hemisphere has summer, it

does not see the Sun as closer and bigger.)  Translated into what we

see on the ground, it means that summer is when the Sun rises earlier

and sets later, and goes higher in the sky at noon.  You can see all

these things with the globe and light setup.  I had had the kids keep

a sketch of the position and time of sunset or sunrise each week for

the past six weeks, and these data match the model I just described.

I'll analyze that in a bit more detail, and explore the Moon's orbit

around Earth, in my next visit to the school.

Turn! Turn! Turn!

This spring I am assigned to work with the Peregrine School 3-4
graders on astronomy, and last Friday was my first day, so I started
with basics like how we know the Earth spins.  We tend to feel
superior to people in the past who believed that the Sun went around
the Earth but, really, how can you use basic observations to show that
it doesn't?  I suspect that most people on the street would be stumped
by this if I didn't allow "satellites" or "NASA" as an answer.

If we only had the observation that the Sun rises and sets every 24
hours, we wouldn't be able to conclude anything.  Each star also rises
and sets in roughly (later we'll see why I say roughly) 24 hours, so
based on pure majority rule, it might be easy to attribute the
apparent motion of the Sun and stars to Earth spinning.  This model
invokes only one thing (Earth) moving, vs the other model invokes a
grand conspiracy of everything else in the universe circling us at an
agreed-upon rate of once every 24 hours.  Sounds like a no-brainer,
but why don't we feel Earth moving?

The kids had lots of ideas in response to this question. It moves so
slowly we can't feel it? No, its circumference is about 24,000 miles
so if it spins in 24 hours its equator must move 1,000 mph.  It moves
so quickly we can't feel it? Gravity?  Centrifugal force? It's so big
we don't feel it move?  There were so many ideas about this that I
decided to explore Galilean relativity: if you are in a laboratory
moving at constant velocity, there is no experiment you can do to
prove you are not actually stationary.  Think about a smooth flight in
an airplane.  If you drop something does it fly backward, indicating
that you are actually traveling at 500 mph?  No, it falls straight
down.  Unless you look out the window, you can't tell that you're
moving---there is NO experiment which will tell you this.  If you do
look out the window, all you can conclude is that you are moving
relative to Earth...there is no experiment you can do that says Earth
is stationary and you are the one who is moving.

This was a pretty new and shocking idea for the kids, so we spent a
long time discussing it.   I remembered a great video I had seen
demonstrating one aspect of this, so I sketched it out and asked them
to predict what would happen.  Say you have a pitching machine which
shoots baseballs at 100 mph, but you mount this machine in the back of
a pickup truck which goes 100 mph the other way.  What will the ball's
speed be, relative to people on the ground? 200 mph? 100 mph?  Zero?
We analyzed this until break time, then after break I showed them the
video.  Mythbusters also did a similar thing, which you can see much more clearly.

The bottom line is that velocities are relative.  So if everything in
your vicinity is moving together at the same speed, it can all be
considered stationary.  This applies to your vicinity on Earth:
although Earth's rotation causes different parts of Earth to move in
different directions and speeds, the part that you experience at any
one time is so small that to high precision it's all moving at the
same speed in the same direction. (When winds move air over hundreds
of miles, that air does eventually feel the effect of Earth's
rotation, the Coriolis effect.)

So not feeling Earth's spin is not a valid argument that it must be
still.  But how do we prove it spins? The Coriolis effect is one way,
but I considered that too advanced for this audience.  Instead, I
explained the Foucault pendulum, which many of them had seen but
probably didn't realize the significance at the time.

Next, we tackled Earth's motion through space.  Spinning is not enough
to explain all our observations, because the stars rise and set every
day slightly faster than the Sun, which means that over time the Sun
loses more and more ground to the stars, and over the course of a year
we see the Sun make one complete circle around the sky relative to the
stars.  What could explain this?  Well, maybe the Sun does go around
Earth, in addition to Earth spinning. But maybe the Earth goes around
the Sun. How could we tell the difference?  I'll get to the bottom of
that next time I visit the school, but for the time being I wanted to
focus on other changes throughout the year and tie them all together
into a coherent model.  I'll post that part of our discussion soon.

A Sense of Scale

Today we covered three small topics.  It's my last day with the 1-2
graders (I will rotate to the upper graders), and also the last day
before Christmas vacation, so I tried to squeeze in several fun things
and also answer some of the questions which arose last week.  So we
didn't go super-deep in any one topic, but we had a blast. 

We started with a movie: the ten-minute 1977 classic Powers of Ten by
Charles and Ray Eames.  I wanted to show this movie because the kids
had many questions last time, when I mentioned galaxies but didn't
have time to really explain them.  This movie steadily zooms out from
a person on Earth to show how big and how far apart astronomical
objects are.  The movie then zooms progressively in to show the sizes
of microscopic things.  (Note: if you want more snazzy modern special
effects you might try the more recent Cosmic Voyage, but Powers of Ten
feels more intense.)  I stopped the movie many times to answer
questions as they arose, but eventually there were too many questions.
We had four 3-4 graders in the room, and I will be doing astronomy
with them in the spring.  It looks like showing this movie would be a
good way to start my three months with them.  They could generate
questions, and we could take our time answering them.  The best
question today was, "How do we know all this?" and I hated not having
time to give a real answer.  My three months of astronomy with the 3-4
graders will be the answer to "How do we know all this?"

I then showed a website for visualizing the sizes of things, where you
control the zoom. This is a great site for showing how much
bigger the Sun is compared to Earth, how much bigger some stars are
compared to the Sun, etc.  But be warned: they do NOT show the space between these objects, so don't be fooled.  The space in between stars
is VERY, VERY BIG compared to the stars themselves. 
Apart from that, it's a great tool.  (One caveat: I did not zoom out all the way to the "estimated size of the universe"...there is no estimated size of the universe.)  Exploring this site also generated many questions, so that may also be a good icebreaking activity.  Because you can zoom in as well, it could even be a good icebreaker for life sciences as well.

A few more links for interested parents:

• http://www.nikon.com/about/feelnikon/universcale/  is a similar idea as the previous link but with a different feel.  It's worth checking out, but it mostly focuses on microscopic things rather than astronomical things (it has a few mistakes too.

• http://www.wordwizz.com/pwrsof10.htm is another site along these lines; it's not as pretty as the previous two, but it does properly show the vast space between things.

• http://www.powersof10.com/ is a site (currently in beta) by the Eames Office. I just discovered while gathering links for this post, so I can't say much about it other than it looks promising.

Activity number two was understanding orbits with a donutapult demo and play with the coin funnel.  Since I've blogged about this before, I won't describe it in detail here.  If you'd like to read about it, search for these terms (donutapult and coin funnel) in this blog's search box.

Activity number three will be the next blog post.

Glaciers, Plate Tectonics, Rock Cycle and Fossils: The Geology and Yosemite

Friday was jam-packed with science this week as Teacher Carol and I
helped the upper graders demonstrate the geology of Yosemite to the
younger children, in preparation for our field trip there.  I stayed
in the 1-2 grade classroom, so I will mostly report from there.

Carol set up four half-hour activities:

• glaciers
• structure of the Earth (crust, mantle, core) and plate tectonics
• [snack/recess]
• the rock cycle
• making fossils

In each activity, the upper graders kicked it off by explaining the
topic with the aid of posters they had made (you can read more about
Carol's work preparing the upper graders on her blog).  The upper
graders knew their stuff but had not been trained in pedagogy, so
Teacher Marcia and I facilitated by asking questions and repeating
explanations with simpler words and examples when necessary.  (Teacher
Marcia was really excellent in this regard!  At some point after
discussing erosion, the movement of rocks came up again and instead of
assuming the students instantly made the connection to erosion, she
asked "Do rocks have legs?"  This was funny but also made the children
stop and make connections to what they had learned earlier.)  Then
each topic turned to a related hands-on activity or demonstration:

Glaciers: we went outside as the upper grades made a block of ice
slide down a "mountain" of sand in the sandbox.  The kids sketched it,
then returned in the afternoon to sketch it after the glacier melted.
The point was to observe the pile of soil and rock left at the point
of the glacier's farthest advance.  We will see moraines like this in
Yosemite.  Often, they serve as dams for rivers which form in the
channel left by the glacier, and thus have lakes right behind them.
This phenomenon of course wasn't visible in the sandbox demo but I
wonder if we could tweak the demo next time so that it is.
  
Structure of the Earth and plate tectonics: we used a hard-boiled egg
to demonstrate a really thin crust (the shell) over a mantle (the
white) and a core (the yolk).  The Earth's crust really is that thin
relative to its bulk!  Slicing the egg in half also fractured the
shell into "tectonic plates."  We further demonstrated different ways
in which plates interact at their edges (convergent, divergent, and
transform boundaries) with pieces of cardboard, paper, and our hands.

The rock cycle: we grated crayons to represent erosion, then we
deposited the grains into a riverbed of aluminum foil.  We did this
for a few different colors to make distinctive layers of sedimentary
rock, then we wrapped up the foil and added pressure (with kids'
hands) and heat (with a torch).  When we opened the foil we found
metamorphic rock!  The torch was my idea because kids love flame, but
it melted the outside without melting the inside, so I would recommend
Carol's original suggestion of a hot-water bath to supply the heat.

Making fossils: we transitioned from the rock cycle to this by
discussing how older layers of rock are deposited first and buried
further down, so we can relate the rock layers to the ages of fossils.
The 1-2 graders are really into dinosaurs, so this was a great
transition: training for dinosaur hunters.  Beforehand, Carol and I
half-filled small paper cups with clay and coated the flat top of the
clay with a bit of Vaseline.  The kids chose from a selection of
animal figurines and pressed their animal into the clay.  They removed
the animal to simulate the decay of the flesh, but the imprint
remained.  Then a mudslide came along (me pouring wet plaster from a
large cup) and buried the imprint.  They took the cups home and
excavated their fossils the next day.

It seemed like a great experience for the kids, but it would also have
been great if it had been a little more spread out, say over two
Friday mornings.  We were asking the 1-2 graders to absorb a lot of
information in one morning!  Teacher Marcia found a good way of
spreading it out after the fact: Carol provided worksheets for the
kids to fill out, but we didn't have time for that because we had to
go slower for the 1-2 graders, so Marcia decided she will use them to
reinforce and review over the next week.  Apparently the 3-4 graders
were able to complete their worksheets in the morning.

The upper graders certainly learned a lot in the week leading up to
this Friday, first learning from Carol (with the worksheets asking
them to articulate their knowledge), and then making posters and
rehearsing demonstrations to prepare for teaching the lower graders.
(If you want to read more about Carol's work with the upper graders,
see her blog.)  However, because the upper graders had no training in
instructive strategies (asking questions, asking students to come up
with additional examples, etc), the teachers in the room had to
intervene a lot (Carol confirmed that this happened in the 3-4 grade
room too) and by the end the upper graders had become somewhat
passive.  I wonder if we could improve this next time by asking the
upper graders to fill a more specific role rather than a general one,
for example each doing a certain experiment or demo which was
self-contained enough for them to feel expert in.  They were certainly
good in helping the kids one-on-one, for example in making the fossils
and, in the 3-4 grade room, in responding to questions asked by the
worksheets.