I was poking around YouTube looking at videos about where the Earth's Moon came from. The currently accepted theory is called the Giant Impact Hypothesis. Though details differ, the main idea is that a smaller planet collided with the early Earth, and the Moon arose from the resulting debris. This hypothesis continues to be tweaked to this day, and other hypotheses continue to be proposed, all because details remain in the existing evidence that are unaccounted for. It's both delightful and a little surprising that the research is still quite active.
I was looking for an up-to-date simulation of the Giant Impact as opposed to an artist's interpretation. I was hoping that, given the current state of computer simulations, there might be something amazing available. There are older videos on YouTube about the Giant Impact which use pretty impressive artist's interpretations. But artists will sometimes take liberties with the physics if it makes the animation more engaging. What I wanted my students to see was a computer simulation that is based on a mathematical model that is allowed to run unedited and unimpeded. Like this:
This is clearly a simulation, probably run on a supercomputer. There is no question that the imagery is based on a model. You can even see the individual elements, almost like little blobs, for which calculations are being run to determine the next state of each blob.
Eventually I came across this video:
I loved this simulation. You can see the resemblance to the one above. The video is obviously a clip from a longer video, but no credit was given. So I hunted and hunted until I found the source:
This is a longer video featuring the work of Dr Robin M Canup, who is also narrating. Dr Canup is associated with the Southwest Research Institute in Boulder CO, where she has used supercomputer simulations to create and build her Moon-formation models. She has also participated in the production of "data-driven cinematic animations," like the one in the video above.
This video is a preview of a portion of a Fulldome Planetarium show called "The Birth of Planet Earth," produced by Spitz Creative Media, the Advanced Visualization Lab of the National Center for Supercomputing Applications, and Thomas Lucas Productions, Inc., set for release in 2019. (More details in this report and in this website).
As nice as this 2018 mini-documentary is, I still wanted just the simulation, so I edited it out of the video as its own clip and stripped the audio. I thought about adding some kind of background music, or using music from the original video. Dr Canup's narration was pretty good, but just not lined up with the simulation clip. I really liked the idea of the female narrator also being the physicist whose work this was - something I'd be proud to point out to my students. So I copied the audio of her narration (with the music), added it to my clip, tweaked the timing a bit, faded the ends, and then had to stall the beginning of the clip to fit the whole audio. I built an elaborate fade-in with the visuals so the stall would feel more natural. It also allows the viewer a chance to focus on Dr Canup before the visual effects of the collision take over. Here is the final result:
A final note: Dr Canup appears in an earlier, similar production created for the History channel in 2007. There's a low resolution version of it on YouTube.
Cross-posted to Teaching Is . . .
Sunday, December 1, 2019
New Demonstrations
A couple of new quick labs for my students this fall. Thanks physics Twitter!
Cross-posted to Teaching Is . . .
I finally bought zcars and had students do this lab - worked great! Thanks for the idea. We graphed a-t using Desmos and later graphed v-t by hand. We used half-second intervals, a little fast for some students who were caught off guard by the acceleration. https://t.co/3xXjdBN8eE
— William H Calhoun (@wmhcalhoun) November 27, 2019
It took an hour or more of digging through a lot of old equipment and odds-and-ends, but I finally did it. Assigned different tasks to different tables: measuring different weights, computing, diagramming, set-up, etc. Thanks for the inspiration! https://t.co/AcvesVcUGF pic.twitter.com/t1yE0b2s4y
— William H Calhoun (@wmhcalhoun) November 27, 2019
Cross-posted to Teaching Is . . .
Monday, August 5, 2019
Stacking all the Planets
You've probably come across this idea that all the planets could fit between Earth and the Moon. The usual representation looks like this image I found on Google:
It turns out, it's not entirely true. Here's a good article about this, published in Slate a few years ago. The planets can fit, but you have to make a lot of adjustments.
What got me thinking about this recently was an amazing video I found on YouTube by yeti dynamics (here's YD's channel). He has made a number of what-if? astronomy videos. The video that astonished me was a simulation of the Earth-Moon system with all the planets fitted inside the Moon's orbit. The view is from the Earth's surface, and the speed is greatly increased. It makes your head swim. But there's something spell-binding about these gigantic orbs circling so close to the Earth (that is, if it doesn't give you motion sickness, like it does for my wife).
What really astonished me is how much work it must have taken YD to construct this. He created his assets (images of planets, background landscape, 3-D modeling), programmed the animation, and created the video using Blender, 3dsMax, and Natron.
I was contemplating this Herculean task when I realized that I already had an application designed for astronomical simulation. It's called Celestia, and I've worked with it for years. It comes pre-loaded with visual assets (and you can simply add more), and the animation programming is done with script files, also included, which are easily modified. Celestia's basic job is to model the known universe, but you can also create alternative worlds, alien star systems, and break the laws of physics.
So I made a copy of Celestia's basic solar system script, and started modifying. I didn't want to disturb our solar system, so I chose a new Sun - 18 Scorpio, a star about the same size and composition as our own Sun. Then I started modifying the planetary data. First, I created a spreadsheet to help me work out the distances and orbital times (also called periods) for the planets. This is where I had to work out the adjustments I mentioned above to fit (or stack) the planets. Here's the list of adjustments:
I took that last point from YD's video. I did try putting the planets in their traditional order, but the visual result was not impressive. This was an inspired move by YD.
Data was obtained from NASA's Planetary Fact Sheets.
Here's a screenshot of my spreadsheet:
This is a 7½-minute video of the final simulation recorded from Celestia. I've positioned the viewpoint in geosynchronous orbit about 8 miles above the Earth's surface, facing northeast, a 50-degree field of view, with the rate of time speeded up a thousandfold.
In case you download and install Celestia, here is a link for downloading a version of the script file I created. You can put it in Celestia's Extras folder, and modify as you wish.
I have shown this simulation to several people. It's quite mesmerizing. As another physics teacher told me, if this is what the sky looked like, we'd never get anything done. My students like it when I project it onto the big whiteboard in my classroom. I'm not sure there is much educational value to it, though. Students seem to recognize that it's "not real," but do understand that the planets would look like that up close. They don't get right away that it's speeded up, and the idea that the planets have been fitted into the Moon's orbit is pretty abstract. Not many people even spot the Moon. Hardly anyone realizes that there's no gravity in the simulation. With gravity, the whole system would collapse pretty quickly. There's no way this could have formed naturally.
But interesting questions do come up, and students like to guess which planet is which, and they sometimes just watch, like you would watch fish in a fish tank. Lankshear & Knobel, in their book New Literacies, describe the role of the teacher as elicitive. In this case, I suggest that, as a teacher, I am being evocative. And maybe that's OK.
Cross-posted to Teaching Is . . .
It turns out, it's not entirely true. Here's a good article about this, published in Slate a few years ago. The planets can fit, but you have to make a lot of adjustments.
What got me thinking about this recently was an amazing video I found on YouTube by yeti dynamics (here's YD's channel). He has made a number of what-if? astronomy videos. The video that astonished me was a simulation of the Earth-Moon system with all the planets fitted inside the Moon's orbit. The view is from the Earth's surface, and the speed is greatly increased. It makes your head swim. But there's something spell-binding about these gigantic orbs circling so close to the Earth (that is, if it doesn't give you motion sickness, like it does for my wife).
What really astonished me is how much work it must have taken YD to construct this. He created his assets (images of planets, background landscape, 3-D modeling), programmed the animation, and created the video using Blender, 3dsMax, and Natron.
I was contemplating this Herculean task when I realized that I already had an application designed for astronomical simulation. It's called Celestia, and I've worked with it for years. It comes pre-loaded with visual assets (and you can simply add more), and the animation programming is done with script files, also included, which are easily modified. Celestia's basic job is to model the known universe, but you can also create alternative worlds, alien star systems, and break the laws of physics.
So I made a copy of Celestia's basic solar system script, and started modifying. I didn't want to disturb our solar system, so I chose a new Sun - 18 Scorpio, a star about the same size and composition as our own Sun. Then I started modifying the planetary data. First, I created a spreadsheet to help me work out the distances and orbital times (also called periods) for the planets. This is where I had to work out the adjustments I mentioned above to fit (or stack) the planets. Here's the list of adjustments:
- The Moon is permanently at apogee (greatest distance from Earth)
- All planetary orbits are circular (zero eccentricity)
- All planets are perfectly spherical (mean radius)
- Pluto is included even though it's not a planet anymore (it fit!)
- All bodies are evenly spaced (1666 km gap between bodies)
- Saturn is tilted 45 degrees so the rings won't slice through other planets
- Planets are not in their traditional order, but in order by size.
I took that last point from YD's video. I did try putting the planets in their traditional order, but the visual result was not impressive. This was an inspired move by YD.
Data was obtained from NASA's Planetary Fact Sheets.
Here's a screenshot of my spreadsheet:
This is a 7½-minute video of the final simulation recorded from Celestia. I've positioned the viewpoint in geosynchronous orbit about 8 miles above the Earth's surface, facing northeast, a 50-degree field of view, with the rate of time speeded up a thousandfold.
In case you download and install Celestia, here is a link for downloading a version of the script file I created. You can put it in Celestia's Extras folder, and modify as you wish.
I have shown this simulation to several people. It's quite mesmerizing. As another physics teacher told me, if this is what the sky looked like, we'd never get anything done. My students like it when I project it onto the big whiteboard in my classroom. I'm not sure there is much educational value to it, though. Students seem to recognize that it's "not real," but do understand that the planets would look like that up close. They don't get right away that it's speeded up, and the idea that the planets have been fitted into the Moon's orbit is pretty abstract. Not many people even spot the Moon. Hardly anyone realizes that there's no gravity in the simulation. With gravity, the whole system would collapse pretty quickly. There's no way this could have formed naturally.
But interesting questions do come up, and students like to guess which planet is which, and they sometimes just watch, like you would watch fish in a fish tank. Lankshear & Knobel, in their book New Literacies, describe the role of the teacher as elicitive. In this case, I suggest that, as a teacher, I am being evocative. And maybe that's OK.
Cross-posted to Teaching Is . . .
Thursday, July 25, 2019
Using Desmos for Physics (Part III)
My inspiration for this project was a Twitter tweet from Brian Frank. In that tweet he showed a photo of a graph sketched out on a whiteboard. It was a graph of a collision between two objects, and it showed the velocity and momentum of the objects before, during, and after the collision, as well as the force the objects applied on each other during the collision.
When considering collisions, one usually compares the momentum before the collision to the momentum after, demonstrating the conservation of momentum. Rarely does one consider what is happening during the collision (it's complicated). What happens during the collision is usually saved for a discussion of impulse, where it is revealed that during the collision the objects exert equal and opposite forces on each other (and this is why momentum is conserved). What Brian had done that was exciting to me was to present it all in one beautiful set of graphs: momentum, velocity, and force, for both objects, before, during, and after the collision.
I decided to model this in Desmos.
I used as my default view a 6-axis view rather than Brian's 3-axis view. I thought that the 6-axis view would be less confusing for my students. The 3-axis view is more elegant, though, so I built a "switch" into my simulation so you could switch back and forth between views.
I have also added other kinds of interaction: the masses and initial velocities can be changed; the collision can be switched from elastic to completely inelastic and back; the time duration of the collision can be changed (impulse!); and there's an adjustable scale which is helpful when the lines all start to overlap.
I added a collision simulation of two balls at the bottom that is timed with the graphs. When the balls collide, they simply overlap, I didn't try to build a realistic collision model.
Here's the link to the project: https://www.desmos.com/calculator/xtr8shdagl
You can minimize the panel on the left (click the "<<" symbol). You can also manipulate the right panel to change the viewpoint.
Using Desmos for Physics (Part I)
Using Desmos for Physics (Part II)
Today was momentum transfer in isolated systems using multiple representations. Here is a look. pic.twitter.com/YHECBOl8fn
— Brian Frank (@brianwfrank) November 2, 2018
When considering collisions, one usually compares the momentum before the collision to the momentum after, demonstrating the conservation of momentum. Rarely does one consider what is happening during the collision (it's complicated). What happens during the collision is usually saved for a discussion of impulse, where it is revealed that during the collision the objects exert equal and opposite forces on each other (and this is why momentum is conserved). What Brian had done that was exciting to me was to present it all in one beautiful set of graphs: momentum, velocity, and force, for both objects, before, during, and after the collision.
I decided to model this in Desmos.
I used as my default view a 6-axis view rather than Brian's 3-axis view. I thought that the 6-axis view would be less confusing for my students. The 3-axis view is more elegant, though, so I built a "switch" into my simulation so you could switch back and forth between views.
I have also added other kinds of interaction: the masses and initial velocities can be changed; the collision can be switched from elastic to completely inelastic and back; the time duration of the collision can be changed (impulse!); and there's an adjustable scale which is helpful when the lines all start to overlap.
I added a collision simulation of two balls at the bottom that is timed with the graphs. When the balls collide, they simply overlap, I didn't try to build a realistic collision model.
Here's the link to the project: https://www.desmos.com/calculator/xtr8shdagl
You can minimize the panel on the left (click the "<<" symbol). You can also manipulate the right panel to change the viewpoint.
Using Desmos for Physics (Part I)
Using Desmos for Physics (Part II)
Wednesday, July 24, 2019
Using Desmos for Physics (Part II)
Here is a variation on the Desmos graph I created in my last post. This graph is intended less as a demonstration and more as a student exercise. The five dots are moveable, and define the position curve. Then by clicking on the Speed circle at line 4 in the side panel, students can see the speed curve, which is the slope of the position curve. This is useful for students learning to read slope by focusing on key inflection points and trends.
Here's the link to this Desmos project: https://www.desmos.com/calculator/vo4kxervvi
You can minimize the panel on the left (click the "<<" symbol). You can also manipulate the right panel to change the viewpoint.
Using Desmos for Physics (Part I)
Using Desmos for Physics (Part III)
Here's the link to this Desmos project: https://www.desmos.com/calculator/vo4kxervvi
You can minimize the panel on the left (click the "<<" symbol). You can also manipulate the right panel to change the viewpoint.
Using Desmos for Physics (Part I)
Using Desmos for Physics (Part III)
Tuesday, July 23, 2019
Using Desmos for Physics (Part I)
When I discovered Desmos, I knew that both I and my students would love it. Desmos has been called an online graphing calculator, which is literally true, but a description that barely captures the possibilities. I have come to see Desmos as a programmable simulator, using a programming language called math.
I could see right away that there would be two ways for me to use Desmos in the physics classroom. First, I could create interactive, animated graphs that students could manipulate and play with. Second, students could, with a little scaffolding, create their own animated graphs. These graphs could demonstrate basic graphing concepts, such as finding the slope of a curve, or building a distribution curve for a set of data. They could also demonstrate basic mathematical relationships among various physical quantities.
But first I had to learn how to use Desmos. The fastest way for me was to find existing graphs that I was interested in, study how they had been built, and then modify and adapt them. When I inevitably "broke" a graph, I was able to find enough information online to figure out where I had gone wrong. It was really fun, and the immediate response by Desmos to any changes was addictive. I also quickly realized that my math skills are pretty rusty. I've done a lot of programming, and you can get away with some sloppiness and inelegance, but straight-out math is pretty unforgiving. If you need to brush up on your math skills, Desmos is the most fun way I can think of to do so.
This is my first Desmos project: https://www.desmos.com/calculator/fm6yuykclr
You can minimize the panel on the left (click the "<<" symbol). You can also manipulate the right panel to change the viewpoint.
Go to line 6 on the left panel (Graph of Slope) and click the circle.
This graph is based on a graph I've already had the students draw and analyze. Students commonly confuse position (the height of the curve) with speed (the slope of the curve), so the more tools for visualizing the better. In this case, I'm using Desmos as a demonstration tool, but it's pretty easy to have all the students call up the graph on a laptop and show them things they can change. I try to have them guess what might happen with a given change, and then check their guesses. Each instance of the graph is separate from the other instances, so students can modify the graphs without disturbing my original or each other. They also do not need to create an account, or even log in. Hit the link and play!
Using Desmos for Physics (Part II)
Using Desmos for Physics (Part III)
I could see right away that there would be two ways for me to use Desmos in the physics classroom. First, I could create interactive, animated graphs that students could manipulate and play with. Second, students could, with a little scaffolding, create their own animated graphs. These graphs could demonstrate basic graphing concepts, such as finding the slope of a curve, or building a distribution curve for a set of data. They could also demonstrate basic mathematical relationships among various physical quantities.
But first I had to learn how to use Desmos. The fastest way for me was to find existing graphs that I was interested in, study how they had been built, and then modify and adapt them. When I inevitably "broke" a graph, I was able to find enough information online to figure out where I had gone wrong. It was really fun, and the immediate response by Desmos to any changes was addictive. I also quickly realized that my math skills are pretty rusty. I've done a lot of programming, and you can get away with some sloppiness and inelegance, but straight-out math is pretty unforgiving. If you need to brush up on your math skills, Desmos is the most fun way I can think of to do so.
This is my first Desmos project: https://www.desmos.com/calculator/fm6yuykclr
You can minimize the panel on the left (click the "<<" symbol). You can also manipulate the right panel to change the viewpoint.
Go to line 6 on the left panel (Graph of Slope) and click the circle.
This graph is based on a graph I've already had the students draw and analyze. Students commonly confuse position (the height of the curve) with speed (the slope of the curve), so the more tools for visualizing the better. In this case, I'm using Desmos as a demonstration tool, but it's pretty easy to have all the students call up the graph on a laptop and show them things they can change. I try to have them guess what might happen with a given change, and then check their guesses. Each instance of the graph is separate from the other instances, so students can modify the graphs without disturbing my original or each other. They also do not need to create an account, or even log in. Hit the link and play!
Using Desmos for Physics (Part II)
Using Desmos for Physics (Part III)
Tuesday, July 16, 2019
New Physics Curriculum
I was tasked this year with redesigning the physics curriculum at my school. Our state (MA) just upgraded their framework, so we needed to re-align. For the last decade, the state's framework was nothing more than a shopping cart of physics topics. There wasn't even an attempt to distinguish topics from concepts. The state assessment required students to have key vocabulary memorized, and to know how to pick out the right equation and apply it correctly to word problems. And that was about it.
My physics team has only three members. For good or for ill, we are all well-versed in the old state framework and assessment. The new framework is mostly based on the Next Generation Science Standards, so it’s quite different. I was excited about the change, because I think the NGSS is a worthy approach. But it’s very different from the old approach, and I wanted the team to have the time and opportunity to adapt. The new curriculum I wrote is organized in a way that looks similar to the old curriculum, but introduces and adapts the new framework language. The team already has a strong bias toward hands-on, project-based, team-oriented classwork. I wanted the physics team to continue moving in that direction, but to shift their conception of this project-based classwork from demonstration-of-topic to phenomenon-model-interaction.
To help our team, perhaps other science teams, and even our supervisors, to better understand the NGSS framework, I created a concept diagram. The diagram is not based directly on the NGSS framework, but is instead a representation of the new curriculum I wrote. I think of the new curriculum as a particular instance of the NGSS framework.
The old curriculum thinking was topic first, application second. The new curriculum flips that around to phenomenon first, model second. The basic interaction is that the phenomenon informs the model, and the model makes predictions about the phenomenon. We choose an anchor phenomenon that is sufficiently complex, has relevance to the lives of the students, and is interesting or engaging. As an aid in exploring this phenomenon, simpler and perhaps more accessible related phenomena are introduced.
The model is related to other models, largely through shared concepts such as force and energy. Through these core concepts, students can develop a picture of physics as a consistent viewpoint and approach to understanding the world, rather than merely a collection of topics. The model is represented and expressed in many ways. These multiple representations give students multiple pathways for exploring the relationship between model and phenomenon.
Finally, in keeping with the idea that learning comes from doing, I include a summary of what students could do as they explore the phenomenon-model relationship. This list is broadly in line with the goals stated in the standards of the new state framework.
Cross-posted to Teaching Is . . .
My physics team has only three members. For good or for ill, we are all well-versed in the old state framework and assessment. The new framework is mostly based on the Next Generation Science Standards, so it’s quite different. I was excited about the change, because I think the NGSS is a worthy approach. But it’s very different from the old approach, and I wanted the team to have the time and opportunity to adapt. The new curriculum I wrote is organized in a way that looks similar to the old curriculum, but introduces and adapts the new framework language. The team already has a strong bias toward hands-on, project-based, team-oriented classwork. I wanted the physics team to continue moving in that direction, but to shift their conception of this project-based classwork from demonstration-of-topic to phenomenon-model-interaction.
To help our team, perhaps other science teams, and even our supervisors, to better understand the NGSS framework, I created a concept diagram. The diagram is not based directly on the NGSS framework, but is instead a representation of the new curriculum I wrote. I think of the new curriculum as a particular instance of the NGSS framework.
The old curriculum thinking was topic first, application second. The new curriculum flips that around to phenomenon first, model second. The basic interaction is that the phenomenon informs the model, and the model makes predictions about the phenomenon. We choose an anchor phenomenon that is sufficiently complex, has relevance to the lives of the students, and is interesting or engaging. As an aid in exploring this phenomenon, simpler and perhaps more accessible related phenomena are introduced.
The model is related to other models, largely through shared concepts such as force and energy. Through these core concepts, students can develop a picture of physics as a consistent viewpoint and approach to understanding the world, rather than merely a collection of topics. The model is represented and expressed in many ways. These multiple representations give students multiple pathways for exploring the relationship between model and phenomenon.
Finally, in keeping with the idea that learning comes from doing, I include a summary of what students could do as they explore the phenomenon-model relationship. This list is broadly in line with the goals stated in the standards of the new state framework.
Cross-posted to Teaching Is . . .
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