A timely addition to the Hewitt Drew-It collection

With flat-Earthers on the rise, it's a good time to review reality. Paul Hewitt's here to help.

Hewitt-Drew-it! PHYSICS 149. Eratosthenes and the round earth
Hewitt presents an easy explanation on how Eratosthenes measured the diameter and circumference of the earth in about 235 B.C. Only simple geometry is used.



For a complete index of Hewitt Drew-It video lessons, start at
Hewitt Drew-It! PHYSICS Screencast Directory

There are quick lessons on virtually all topics covered in introductory physics, conveniently organized for easy access.

Making engagement visual

At semester's end, it's possible to look back and see how student engagement in the course manifested itself into semester grades.

Students who perform well on tests and labs naturally percolate to the top. But those who don't excel in those objective measures have alternate routes to good grades in my courses.

During the semester, "extra credit" (credit toward the final: CTF) is awarded in dribs and drabs for various tasks and in-class competitions. Completing paperwork associated with the beginning of the school year and team performance in our egg-toss competition are typical first-semester sources. The credit is accumulated through the semester, but only becomes active as an addition to the final exam score. Some teachers add in extra credit as it comes in. That leads to disappointment when final exam scores are low. Adding it to final exam scores at the end of the semester leads to delight similar to finding money under the cushions of the sofa/couch/davenport.

More importantly in my Physics (PHY) and Conceptual Physics (CP) courses, students can earn back points lost on unit tests. The process is called Test Correction Journal. Students write "journal entries" for each item they missed on a unit test and reflect on why they were drawn to a wrong answer over the right answer. Later, a quiz is given consisting of questions from the original test. If they get 10 out 10 on the quiz, they earn back half the points they missed on the test. If they 9/10, they get 90% of half the points they missed, etc.. A 60 can turn into an 80 and 40 into a 70. A 90 can turn into a 95. The more help you need, the more help TCJs provide.

Neither CTF nor TCJs depend on rapid assimilation of course content. But they do depend largely on engagement. Sometimes students who miss many items on a unit test cannot finish the journaling process that we begin during class time. They need to come it at lunch or after school during an approximately two-week window to finish the journal. Only students with completed journals are allowed to take the quiz that will earn their missed test points back.

Students who disengage from TCJs create and expand a gap between themselves and those who are engaged. My engaged students earn only As and Bs. But Cs, Ds, and Fs are given every semester, as many students elect to disengage.

The listings below are actual student data. Each is a period, sorted by points earned. I used Excel's conditional formatting to color the cells in a spectrum from top-score green to bottom-score red, with yellow in between. The next column colors CTF points on a same basis (green good; red bad). Then (for PHY classes), it's the TCJ column with the same color scheme. The last column shows the final exam raw score out of 50. The top number in each column show the maximum value possible.

The pattern is fairly consistent, with anomalies here and there. Nothing to shatter the Earth here. I just wanted to see how well the seemingly nebulous "engagement" tracks to overall class performance. Teachers know this pattern is really the only one that's possible. Students don't always have an intuitive understanding of it. Some will see the evidence and reject it nonetheless.

Those students believe it's possible to get a top score with minimal engagement. It's mathematically possible. It just never happens. They may also fear that investing in full engagement will not be rewarded in a top score. Yet we don't find a red Points value followed by green CTF and TCJ columns. That's actually much less mathematically possible, given what TCJs do.

Fun does not mean unprofessional

I follow some great educators on Twitter, one of the great things about the platform is being able to find people that share interests that I don't know personally. I like to follow inspirational teachers that make me want to do better, that can expand my point of view and remind me that how varied and diverse our national education system is. I get a lot of great ideas from physics teachers and get to chuckle in commiseration with hashtags like #teacherlife and #teacherproblems.

Two days ago a math teacher and author from New York Jose Vilson posted a video of himself dancing in class with a great Christmas sweater. I liked it, not thinking much of it and continued to scroll. Unsurprisingly, Jose's video was retweeted by other people I follow so I got to smile again every time it came up:

When you’re a teacher about an hour away from vacay and take off the professionalism for a minute pic.twitter.com/6AYlvfDznP

— José Luis Vilson, NBCT (@TheJLV) December 22, 2017

I was surprised however, when I started noticing that not only were people retweeting the video but also including remarks of defense and support. I had to follow a few threads to figure out why Jose even needed to be defended. (Hint: he shouldn't have to be) There had been comments about Jose's dance being "unprofessional" but they weren't so nice about it, in fact they were downright racist about it.

Keep America Racist Forever. https://t.co/rxs6oz2YU6

— José Luis Vilson, NBCT (@TheJLV) December 23, 2017

On one hand, 2017 can't shock me much more but on the other, he was just dancing! He is a great teacher and activist, published author, etc. but that doesn't mean he's not human. Teachers are human. We are not robots, we are people. The whole thing got me thinking of all the times I've been "unprofessional" in front of my students. Its quite a list:

- Teach students to do the "Superman" yoga pose and worn two back packs at a time while teaching center of mass and stability.
- Literally kicked off my heels to run across my classroom and try to race the stadium wave my students make across the classroom while teaching, duh, waves.
- Spun around like a ballerina/ figure skater to remind them about conservation of angular momentum.
- Spun and leaped in a circle to reinforce the difference between rotation and revolution.
- Stood on lab benches to drop/ throw/ launch a variety of projectiles.
- Channel my inner drill sergeant and lead the class in force exercises; I say "A Force is a what?" and they respond "A push!" I say "And a what?" and they shout back "A pull!"

There are probably more that I've forgotten. As many other teachers have I also frequently share jokes and puns about my curriculum. Students' suspicions are correct, teachers do actually plan some of those jokes. I have a construction hat I've written the formula for work on and I wear it every year. This year I made a giant piece of buttered toast just to illustrate a tough textbook problem

Teachers often use humor to teach and engage their students. We've been known to use comic strips and Dan Burns even dresses up to look like the physics teacher in FoxTrot on occasion.

All of that is acceptable, but dancing is not? You've undoubtedly heard the phrase "Happy Dance," when someone does a little dance for about 10 seconds when they are unexpectedly happy. You may see your students do a happy dance when they got a grade higher than they expected. I've seen full grown adults do a happy dance in a store when they find their favorite wine on sale. The point of the happy dance is spontaneous joy, despite surroundings, in order to celebrate something unexpected or surprising. How is that accepted across our culture but a teacher in a classroom of happy students can't dance? Being fun does not mean you are unprofessional. I say teachers continue the dancing, winging, joking, etc. This job is hard enough without being a sour puss.

An inclination for serendipity

When I show the Honda Cog ad (flavors of equilibrium, energy transformations), there is always strong skepticism regarding the wheels that roll uphill. So I am always ready to go with the demonstration illustrated in this previous post.

Sometimes I leave the wheel resting comfortably on the inclined plane. That very same inclined plane is also home to my electronic balance.

So why not another Physics Mashup?

First, students should be able to explain why the wheel holds fast on the incline before I spill the beans. Or in this case, ball bearings.

Next, I tare the scale and rest the "hill-hugger" atop the scale. A reading is observed.

Finally, students should correctly predict what will happen to the scale reading when the incline is re-leveled. Assure them the wheel will remain atop the scale.

It's not so novel it will shatter the Earth. But it's nice to milk some mileage out apparatus just otherwise lying around.

The answer can be seen via the comments. I leave the solution to the reader.

Advanced Studies in Artistic Lightning

Watch it big; watch it loud. But mostly, watch it.

Transient from Dustin Farrell (www.dfvc.com) on Vimeo.

And remember, deviations from physical realism serve not as disqualifies, but springboards for discussion here.

Can you feel the inertia?

I just started rotation in my AP Physics C class and I introduced moment of inertia today. There was the traditional hoop vs disk down a ramp and I found an inertia stick for students to observe. The first class went very poorly because I introduced the rolling inertia demonstrations before we had talked about rotational kinetic energy and rolling ... BUT I did develop a new demo that did work so let's focus on that.

My textbook has a lot of pictures like this one of unusually shaped objects:

The odd objects are meant to illustrate that the moment of inertia is different with different axis positions. This concept will also help explain the Parallel Axis Theorem if the object is not one of the uniform shapes commonly seen on a moment of inertia chart. I wanted to make something like this with a movable axis so that my students can feel the difference in inertia at different axis points. Its a good thing I have a mini-shop in my prep room ...

I found a scrap piece of 3/4" plywood and used a bandsaw to cut it into an "odd shape." Then I drilled three 1/2" holes through it, one on each end and one roughly at the center of mass. I cut three 8" pieces of 1/2" dowel, one for each hole. The dowel was snug enough that when you rotate it, the whole piece rotates.

The wood is hefty enough that you really feel a difference from the center axis to one on the end. You can feel a slight difference between the two ends but not as much as I'd like. I may carve out a bit more so that the difference is easier to feel. Below is a video of me spinning it to give you a sense of it. 

Catch and Splash: Grass Omelette XVII

After a few year's dalliance with Energy before Momentum, I have switched back to Momentum before Energy. Please don't flame!

One benefit to the return is that our annual egg toss competition, Grass Omelette, has returned to late October/early November. And that increases the likelihood of nice weather.

We conduct the event prior to any discussion on impulse so that we can refer to it during or after our lessons on F∆t = m∆v.

I shoot the catches at 120 fps so that I can pull half-decent still images of "splashes" to give to the individual students who were brave enough to don the plastic ponchos and kilts. I'm currently using a Panasonic Lumix DMC-FZ200. Maybe in the future, I'll shoot normal-speed 4K video to get better stills. At some point, consumer high-speed 4K will be available. I know the Sony RX10 iv can shoot 24 fps at full resolution (as well as 960 fps lower-res high-speed).

In any case...

Egg Toss 2017 Catches

Egg Toss 2017 Splashes

When I had 5 sections of Physics (no AP anything and no Conceptual Physics) in 2013, I had enough to produce an amusing compendium set to Vangelis' Chariots of Fire.

Egg Toss 2013

Simple demo big gains

I have noticed a big difference in student comprehension when the problems become real to them. Simple visuals can have a big impact on the students "getting it." I can't count the number of times I've tossed a tennis ball around to make a point. Somehow holding the tennis ball at different heights or just tossing it up to catch it again can lead to "Oooh now I see what's happening!" So I have several simple demos that help students visualize their problems, a block or two hanging from the ceiling with spring scales, a stuffed toy in a bucket, etc. 

When we studied springs I found a Pasco spring demo set with five springs all of the same length but different spring constants. The first stage was to hang a 20 g mass from the red spring and see it barely settle above the table. I asked students what would happen if I were to hang a 500 g mass then from the green (which they assumed was identical). They were surprised at its shorter elongation and when I asked why they all said "it has a larger spring constant."

For the next stage I set up two large ring stands with another bar clamped horizontally between them. I dramatically assure students it is level with the springs hanging at their relaxed length. Then I hang a 500 g mass from each and they can see the slight differences in elongation. Then the 500 g masses are switched out for 1 kg and the difference between them becomes more pronounced (left). Applying this to Hooke's Law they could all calculate the spring constant for each spring. But this made it way more interesting than five given forces and elongation lengths to calculate the spring constant from a word problem. 

When my AP Physics C class started center of mass, many could calculate the center of mass with equations but had a hard time visualizing what that actually meant. A common problem involves materials of different densities stuck together, for example a piece of aluminum and a piece of iron. To make a real life version I found a piece of Styrofoam that was the same thickness as a piece of scrap wood. I drilled three holes in the wood, stuck three dowels into the holes and stuck the dowels into the Styrofoam. I wrapped the whole thing in paper to make it appear uniform but I did tell students it was made of two different materials. I showed it to students and asked what information they would need to solve for the center of mass. Of course I play with them a bit and after each response I say, "Ok, now you can solve it right?" to which they predictably respond, "No, we need XYZ too!" Eventually, I give them the dimensions of the whole thing and let them solve for it. The dimensions are listed on the paper below (the "total mass" includes the paper in case they ask).

They are not surprised that the center of mass is closer to the wood side but they are surprised that for this particular arrangement it's actually on the wood. It's a simple practice problem but once they're done I can balance the piece on my hand at (almost) the exact position they predicted, about 5 cm in from the wood side. Students that struggle with this homework problem were successful with this in-class practice problem. 

Another simple one my colleague Jessie Chen shared with me can be done by every student in your class on the cheap. Like less than $1 cheap. Most dollar stores sell packs of cards for $1, or even a double pack if you're lucky. Each student will need one plastic playing card (or index card) folded at a right angle along the length of the card. Place it on the corner of the table with one corner hanging off the edge of the table. Place two pennies on the card so that one is on the portion on the table and one is on the portion hanging off the table. You can use a pen or pencil to press on the card so that when it moves it pivots around that point. Flick the vertical part of the card on the side that is hanging off the table. This causes the card to move so that it is no longer supporting the penny hanging off the table and it will fall straight down due to gravity. On the other side the vertical portion of the card will push forward, applying a horizontal velocity to the penny and making it shoot off the table in a half a parabola shape. You can hear (and see) the two pennies hitting the ground at the same time. Many of us have a fancy machine that demos this for us, sometimes called a "Drop/shot" or a Newton's Second Law machine, and those work great, don't get me wrong. But to be able to hand these to my students and have them try it, nothing can be better than that! 

Trick or treat? See for yourself

It's been a little quiet around here for a variety of reasons. So let's shake off some dust for ... Halloween? Why not?

Four drops of food coloring are added to the center of a half-filled "skinny fish tank" (a.k.a., Arbor Scientific Laser Viewing Tank) resting on a low-friction turntable (Pasco's Rotating Chair platform).

The tank is then given a spin. And, well..?

It made me say those magic words all people in science prize: "That's funny!" I didn't know what to expect, so in some ways, this wasn't overwhelmingly surprising. Still though...



I get the parabolic surface. But what's going on in the dye? I'm sure there's a lovely, simple explanation that I should know. But I don't.

If you do, kindly leave it in a comment. I am your student.

Don't Ask Smithsonian

My in-laws gave me a subscription to the Smithsonian magazine a few years back. I don't read it as regularly as my Sky and Telescope and Aviation Week subscriptions but I do get around to reading most of them. I enjoy history, especially the small forgotten details that have unforeseen important impacts. The Smithsonian is full of such stories. The most recent issue I read was September 2017. I read about Chick Parsons, a pivotal figure in the guerilla war in the Philippines during WW II, speculation that a disagreement over smallpox inoculation estranged Ben and Deborah Franklin, and Benjamin Lay, one of the earliest Quaker abolitionists. There usually is a science or technology article. This issue had an excerpt from Scott Kelly's new book about spending almost a year in space.

At the end of each issue is the "Ask Smithsonian" page. Readers send in questions that are answered by a bullpen of Smithsonian-connected scientists. It is hard to believe that a column like this still exists in this age of instant Internet searching, but it is entertaining to read. Perhaps the people who are most likely to send in a question to a magazine are the least likely to know how to do a key word search. In the September issue the first question was "In how many ways can snake venom kill humans?" Hopefully this was not a time sensitive query. The reply by Matt Evans, an assistant curator at the National Zoo is thorough and encourages further research with the brief mention of "complex venoms". At the end of each column is an invitation to submit queries to Smithsonian.com/ask. 

The first exhibit in support of the harsh title of this post is a question in the November 2015 Smithsonian from Stan Pearson, Newport News, Virginia. Stan asks, "Why do astronauts aboard the International Space Station seem to float? The ISS is only about 200 miles above Earth—where, according to Newton, gravity is almost as strong as it is here on the ground." Stan's question was answered by Valerie Neal, curator of space history at the National Air and Space Museum. Dr. Neal starts off well when she replies, "They experience weightlessness not because of a lack of gravity but because the ISS, and they, are orbiting Earth in constant free fall." 

Invoking free fall to explain the sensation of weightlessness is helpful. It connects the questioner to experiences they have had like jumping off a diving board or jumping on a trampoline. There is no difference between those experiences and orbiting except that your path intersects the Earth's surface while that of the space station does not. I prefer to use the expression "apparent weightlessness" because I define weight to be the force of gravity on an object. Not everyone uses this definition. Some define weight to be whatever a scale reads. Therefore, I won't list this as a mistake. 

Dr. Neal continues, "They’re falling toward Earth and moving forward at about the same velocity." 

It can be useful to consider an orbiting object to be falling toward Earth but this statement is just plain wrong. In a quarter orbit it moves "below" its initial position by a distance equal to the radius of the orbit. In the same time it moves a quarter of the orbit's circumference. This distance is pi/2 greater so the velocities are not the same. Since the directions are different, the term speed should have been used, but making something wrong less wrong is of questionable utility. 

Dr. Neal then adds, "Because the downward and forward forces are nearly equal, the astronauts are not pulled in any specific direction, so they float." 

There are no forward forces in a circular orbit. Neglecting drag, there is only the force of gravity and it is acting down. An elliptical orbit would have a component of the force of gravity tangent to the orbit. Since this question is about the ISS and its circular orbit, that is not applicable nor would this help Dr. Neal. This statement is nonsense and makes me wonder where she learned about gravity and orbits. 

My next exhibit for why asking Smithsonian can be problematical is from the March 2017 issue.  This one can't currently be found online but I have the print version. Joseph A. Leist from Hamilton, New Jersey asks "Why doesn't Saturn's gravity pull its rings crashing down to its surface?" Matthew Holman, senior astrophysicist at the Harvard-Smithsonian Center for Astrophysics answers, "Saturn's rings are composed of billions of particles of rock and ice from broken-up comets and asteroids that are orbiting the planet like so many tiny moons. Those particles, orbiting at speeds of 20,000 to 40,000 mph, sometimes collide with one another, but they don't come crashing down onto Saturn's surface because the centripetal acceleration of their orbits balances out the planet's gravitational pull." 

He muddles the issue with the mention of collisions. It is certainly possible that a collision would send a particle crashing onto the surface but since nearby particles have similar velocities, the collisions are not violent enough to result in a large enough change in velocity. Dr. Holman veers away from the laws of physics when he tries to explain why the particles stay in their orbit regardless of any collisions. Acceleration and force are related but they are different quantities. They cannot ever be equal. It also is puzzling how they would balance each other out when they are in the same direction. Centripetal means toward the center and the force of gravity from Saturn is toward the center as well.

One explanation for why objects stay in orbit is that the centrifugal force is balanced by the force of gravity. This is a very common explanation because it is brief. However, for people that know little about physics it is devoid of information. This explanation is from the accelerating frame of reference of the orbiting object. If you were in this frame of reference you might believe there is no acceleration and conclude that the sum of the forces on you must be zero. Since you know there is gravity pulling down, you would postulate an opposing force in the outward, or centrifugal direction that balances gravity. There is nothing wrong with this point of view but analyzing motion from an accelerating frame of reference is not a trivial exercise. It is best to first understand orbital motion from a non-accelerating frame of reference. The ring particles are accelerating because the direction of their velocity is changing. Their orbits are stable because they have just the right velocity and distance from Saturn that results in an acceleration that is equal to the force of gravity from Saturn divided by the particle's mass. Put a particle at this velocity closer to Saturn and it would start to move toward the surface because the force would be more than what is needed to cause the centripetal acceleration.

Dr. Holman was given a second chance to answer this question when readers responded to his original answer in the May 2017 issue. Their response was summarized by the Smithsonian as "Some readers thought the March “Ask Smithsonian” should have stated that the acceleration of Saturn’s rings was “centrifugal,” not “centripetal,” as printed." He boots this opportunity to correct himself by responding, "Perhaps I should not have written ‘balances out,’ because it is easy to misinterpret. But the force is indeed centripetal. An object in circular motion with a constant speed v and a radius r about the center it is orbiting has an acceleration a=v^2/r that is always directed toward that center. That acceleration is centripetal.”

It appears he didn't bother to read his initial answer. He didn't mention centripetal force in his original response. Why would he say "the force is indeed centripetal"? He appears to cite a quickly searched definition of centripetal acceleration and once again confuses force and acceleration. If you put the entirety of both responses together, his answer is meaningless.

None of this is surprising to high school physics teachers. We are used to scientific publications and websites getting things wrong, especially on the subject of orbits. Sometimes this is because the person does not understand orbits. However, the author is often someone who does know better and the frequency of these erroneous explanations is too high to explain it away to incompetence. I think it is due more to laziness. It is far easier to say the centrifugal force is balanced by the gravitational force than to explain it from a non-accelerating frame of reference. When writing an article about the space station it is easier to use the terms zero gravity and weightlessness than to explain how astronauts are actually in free fall. This is understandable for an author that is frequently writing about such topics. The flow of the article will be affected if they have to explain everything from basic principles every time. Perhaps that is what motivated Phil Plait, the Bad Astronomer, to write a short article about his views on centripetal Vs centrifugal force.

Most physics teachers would disagree with Dr. Plait's position that there is no difference between forces and fictitious forces. The latter arise in accelerating frames of reference and can be useful for analyzing motion, especially circular motion. But they are not real forces. Here is a counterpoint example using linear motion. I am sitting in an airplane as it starts to accelerate down the runway. I might explain the sensation the following way. I think I am not accelerating because I can look around the plane and see that the other passengers are not moving relative to me. Since I feel the seat back pushing forward on me, there must be some other force pushing on me in the other direction to balance this force, resulting in my zero acceleration. I will call this force the "ventilabis retro" force and say it is as real as any force I have ever encountered. This is exactly what Phil Plait writes to make the case that the fictitious outward force on a passenger in a car when taking a turn is real. The key step is to mistakenly conclude there is no acceleration. Thinking there is no acceleration in a turn is more common because many people do not realize that acceleration can result from changing direction, not just changing speed. If the car passenger knows this, they think the car door is pushing in on them causing an acceleration, just like any airplane passenger knows there is only the seat back pushing forward on them, causing an acceleration during takeoff.

I understand why Ask Smithsonian gets things wrong when answering questions like these. They feel compelled to ask an expert with impressive credentials to answer the questions. This often works but not when it comes to explaining something from introductory physics. An astrophysicist from the Harvard-Smithsonian Center for Astrophysics is far removed from his introductory high school physics class. They are unlikely to have ever been asked to explain basic physics to a lay person. They speak from authority and are uncritical of what they write because they believe they will not be challenged. I don't fault them for this. I fault the Smithsonian and their tendency to put credentials above experience. It would be OK to ask Smithsonian if they would ask someone more qualified to answer their physics questions, a high school physics teacher.

If you are a high school physics teacher, I suggest you give one of the questions to your students. Select the best 3-4 answers and mix them up with the response from the expert in Ask Smithsonian. Hand them out and have your students try and pick which response was from the space history curator or the astrophysicist. The results will be surprising, or perhaps not.

A Natural

Due to a crazy start of the school year I've had the "opportunity" to work with half a dozen subs since August. Out of four Physics teachers, we're down to two. One position remained unfilled for the first 6 weeks, another teacher was out with a broken collarbone and subsequent surgery. Luckily a long term sub was procured for one room since the start of school, let's call him Mr. D, so those students have had some consistency. In the other there were a few different subs for two weeks before a recent graduate and alum, Ms. G,  came in in the clutch to help us out for four weeks. Both of these teachers have different styles, neither have a degree in Physics, and yet they were fabulous. I found myself describing both as "a natural." Facing different subs in the future, (recent graduate has to go start her first job, the other is approaching 30 days of the emergency clearance) I'm reflecting on what these two had that made them so great. Its hard to teach new teachers some of the nuances, little tricks of the trade that experienced teachers have. You may find yourself watching a great teacher and can't quite put your finger on what makes them make it seem so easy. But, I'll give describing it a shot:

Command of the room:

This is not to say that when a teacher talks the room is silent, but it might be. This does not mean they are yelling, they shouldn't be. This means that when the teacher talks, the students listen. Not out of fear, but out of earned and mutual respect. Students understand that the teacher has something to share that is important and that they will have their chance in turn. And that's an important piece not often included. Teachers that talk all the time will not have students that listen all the time. Sometimes I find the less I talk, the better they listen when I do. Mr. D has an almost theatrical presence in his classroom, outlining the day's tasks from their agenda never sounded so intriguing. 

Command of the room does mean that you can recapture the room's attention when you need it. I imagine this is more difficult in a science room than in most other disciplines because of the nature of labs. Students are focused on their task, talking with other students (for better or worse) and often not facing the teacher. A necessary management skill is to be able to quickly get students to transition their focus from their own tasks back to the teacher. Without yelling, don't yell. Mr. D does a countdown, "If you could take ten seconds to finish your thought before looking up here. I'd like to see all eyes in 5, 4, 3, 2 .... and 1." You can tell a new teacher they should do that, you can give them the three bar chime we all have but being able to execute it successfully is a skill.

Eyes in the back of their head:

While our students might swear we are biological freaks in this way, we are human. Just humans with heightened and acute sense of awareness. Teachers often have a hard time focusing on single tasks because we never do. At the moment that we are speaking to the class our mouth is almost on autopilot, delivering a sentence we thought of moments before, because our active brain is focused elsewhere. A student in the third row, left side, has his math homework out. A student in the back is playing with his hands in his lap again, you're hoping its a phone. And dammit where did you leave your water bottle? Those moments you turn around to face the board you hear the creaks of chairs or the whispering from one to another and you can tell which side of the room its coming from. You make an educated guess that because its third period its probably James, because its always James. In nature programs you'll often see prey on high alert, head on a swivel, ears rotating even faster, eyes darting side to side. Teacher have to have these prey-like instincts, looking at anything and everything in their classroom.

With multiple one or two day subs prior to her arrival, Ms. G walked into a room of wild students. Within a few days she got to know the students well enough to make gentle reminders about the phones, homework, talking, etc. as if she had years of experience. Mr. D asked about a stain on the floor of his room and could confidently say it wasn't there after 2nd period but was there when he returned 4th period. I know veteran teachers that say, "Huh, I never noticed we had this poster up." Situational awareness is key.

Fly by the seat of your pants:

There aren't many jobs that require careful planning of potentially months (for purchases) or at least days (for copies) that can all be thrown out the window at a moment's notice. Oops, there's a rally you forgot about. Or your copies didn't come in. Or the district wide internet is down .... for a week. Or you just sick enough not to come in, because otherwise you still would (sub plans aren't worth it). As a new teacher, a survival method is often to adhere to the schedule no matter what. If you vary today who knows how you'll have to change the rest of the week! You can't take that sense of not knowing! More experienced teachers are often more flexible, they've had to learn over the years; and it does usually take years. You have to learn when to adjust things to alleviate stress on the students (they need more time for a test) or you (you need more time to grade that test). Sometimes you just don't know how to change that group work into an all class demo that's faster, but you'll learn. 

I wrote the sub plans for Mr. D and Ms. G. I sent them emails a week at a time with all the material they needed, schedules, rubrics, samples, extra background so they could learn the material, etc. I stressed them keeping to the same schedule for my benefit, to keep consistency across all classes and to make their lives easier. And 80% of the time that worked. But we found that Ms. G was a bit of a faster lecturer, so she wrote some sample problems for students to practice solving on the whiteboards she found in a corner. Mr. D had a great way to orally review the vocabulary with the students and didn't get to an activity so he found a way to work that content into the discussion. I checked on them both a few times a day and they would give me updates, "We got to this but not this, so I did this instead," etc. Each time I was pleasantly surprised at their excellent choice, they handled small curricular adjustments like a vet. Copies didn't come in? No problem, let's project it and go over it together. No one did the homework? Take some time, turn to a neighbor and work it through together, we'll add it to the classwork list. Flexibility and creativity are a must for a successful teacher. Immobility is a detriment. 

Knowing what they know:

Teachers make and give assessments to students so that we know what they know. Students often think they are punitive of course but I usually tell my students "You and I both need to know what you know right now, so that we know if we can move forward." Assessments should be as much for the student as the teacher and have as much benefit. After a week or so into Mr. D's take over of the class his students had a quiz. Ms. G teaches the same class, had an additional prep and was put in charge of grading it. Mr. D came into the room very excitedly, "I think they did well! Can I see?" and in a very teacher-heart warming moment they looked at the assessment together. They pointed out this or that student's pitfalls, noting "Yeah, he's had a hard time with that GUESS." or "His 504 said he would have trouble with vocabulary." He was visibly disappointed in some, "But we talked about that one just yesterday!" Which leads me to the next point...

They care about their students:

Written on plaques for teacher desks and in gifs the world over, teachers should care about their students. They should want them to be happy and healthy citizens, protectors of the world of the future. We should be invested in helping them build their future selves, supporting their complex backgrounds and making them feel like they can do anything. This goes beyond someone being a "people person" or not. You don't have to be a touchy feely huggy type either. But you do have to be genuine. You can not fake caring about your students, they'll know. 

Both Mr. D and Ms. G walked into their positions as substitute teachers, they had a finite end date from the beginning. Yet both stopped referring to the students as "Mr. [so-and-so's] kids" and started referring to them as "my kids" very quickly. They came to own those classrooms and those students, caring if they did well, concerned if they were struggling and elated when they succeeded. Ms. G left us yesterday, almost a week before the student's next test. Not only did she get all her grades in order, she wrote a long email to the next sub with information they would need. Included were notes about individual students: "[Name] gets frustrated easily, give him a moment outside and he should come back in refocused;" or "Watch out for [Name] in 3rd, he never stays in his lab group." Ms. G wanted to see the test students would take next week, the lab she would not manage and their last review activities. She wanted to see that they were ready, that they would be able to ask questions, etc. She is worried about a group of kids she will never see again and about how they will do on one test of many in what is no longer her class. You can't teach a new teacher how to have that level of investment in their kids. 

As each of their time in my building comes to an end I am thankful to have worked with Mr. D and Ms. G and hope to do so again, however unlikely. Mr. D is our resident sub now but he's technically an English teacher; I've tried to pull him into Physics but he laughed at me. Ms. G is off to the corporate world but I'd like to think she'll be back. I think she's got the teaching bug and was just too good to stay out of it. I worry that my next few subs will have all the characteristics I dislike: yelling to get students' attention, obvious disinterest in them, ignoring them, etc. I've had subs fall asleep in their chairs, read books all day or actually tell the kids, "I don't care what you do as long as you're quiet." While we give substitute teachers a bad time because we have seen too many as I just described, there are a few good ones out there. May you find a sub that works for you, and better yet, makes the kids say, "Aww not Mrs. [so-and-so], she'll actually make us do the work!"

Jearl's bottle overfloweth

The ringmaster of the Flying Circus of Physics is at it again. This time, Jearl hops into brewery for a beer. Root beer, that is. A former student taps the top of Jearl's open bottle, and physics ensues. Take a look.

Flying Circus of Physics: Bottle Tap (Episode 3.1)


The Flying Circus of Physics now has a YouTube Channel. I recommend subscribing!

One parent that should never be called back

I received an email from my office staff indicating a parent had called and wanted to talk to me, but I was teaching at the time. The parent requested I call her back.

When I did, it turns out she was a telemarketer keen to offer me a private business group travel "opportunity".

"I'm sorry: what is the name of your son or daughter enrolled in my class?"
"I don't have one."
"So you're not really a parent here, are you?"
"I have children."
"I don't appreciate your deception and am not interested in your opportunity."
"Do you know another teacher who might be interested?"
"If I did, I would not tell you. As we speak, I'm composing an email to my colleagues warning them of your deceptive tactics."

Thus ended the conversation. The email was sent out shortly thereafter. The blood pressure remained high for some time.

I get it: times are tough in the world of group travel sales. Maybe. But posing as the parent of a student to a teacher in order to trick them into calling you back is beyond the pale. It disrespects what we do and our commitment to maintain communication with parents.

I cannot imagine this tactic works for her, but if it doesn't why does she do it? She presents an example for those who consider "business ethics" to be an oxymoron.

Total Eclipse of the Sun - Part 4

This post concludes my four part series about total eclipses of the Sun. Part 1 described my first total eclipse experience, part 2 gave advice for observing eclipses and described my second total eclipse, and part 3 gave details of my preparations for the 2017 total eclipse. They are not necessary reading but you may enjoy taking a look at them. I will describe my trip to Madras, Oregon and the activities and events leading up to totality and just after. Much of it should be of interest to physics and astronomy educators. If you are all about the totality, I understand. Just scroll down to the picture of the total eclipse. All pictures and video were taken by myself unless otherwise noted.

Having path of totality cross the campus ensures having a great summer! Climbing tower loomed over volunteer campsite

My wife and I started driving from Los Altos, California to Madras, Oregon, about 10:30 AM on Saturday. The rest of the staff and volunteers at the Lowell Eclipse Experience were arriving Friday and Saturday and I wanted to join them. We were met by Rich Krueger, a physics teacher at Flagstaff Arts and Leadership Academy, when we arrived at Madras High School. We quickly pitched our tent in the volunteer area and were asleep by 11:00 PM. I woke up just before sunrise and noticed an osprey nest in the climbing structure next to our campsite. I wondered if it was occupied. While observing sunrise from the bleachers, I heard the ospreys chicks start cheeping just as the sun struck their nest. The adults quickly flew off to find some fish. Watching the four adult ospreys try and keep the chicks satisfied with fish was one of the highlights of the trip. We noticed when they brought a larger fish back, they would eat the good parts first before giving it to the hungry chicks.

H-alpha could see through clouds but would corona shine through?

Shot through iPhone good enough to show facula and prominences

Sunday was spent setting up the booths and displays for the Lowell Eclipse Experience. There were vendor booths from Lowell Observatory and Madras High School. There were activity booths from Northern Arizona University and Lowell Observatory. There was a group with several types of solar telescopes including a calcium line filtered scope with video display. The Science Channel had a stage for broadcasting live and a booth for free photos that used a green screen to put you in the total eclipse. The auditorium was set up to host talks by the Lowell Observatory astronomers. I set up my h-alpha solar telescope on my tripod and a Skywatcher clock drive. The clock drive only works well if you polar align it. This is difficult in the daytime but I had read about a trick in Sky and Telescope. Open an astronomy app that displays the night sky, I use "Night Sky". Place the phone flat on top of the Skywatcher and adjust the azimuth and elevation until the south celestial pole is centered on the screen. This worked beautifully. I could leave the scope for over an hour and the sun would stay in the eyepiece. I spent most of the day showing mostly staff and volunteers the chromosphere of the Sun. There were some awesome prominences all around the Sun. One extended an unusually large distance from the Sun. Unfortunately, it dissipated before totality. Sunspots don't show well in an h-alpha telescope because they reside on the photosphere. The line of about 3 sunspots that showed in white-light filtered scopes were faint except for the umbra of the leading spot. That proved useful because it was about the diameter of the Earth, allowing me to put the other features in perspective for people. One feature that did stand out was the facula that appeared as a bright stripe over the region where the sunspots were located. Sunspots occur in regions where the solar magnetic field is stronger and inhibits convection. They are a little cooler, thus dimmer than the photospshere. The energy still has to reach the photosphere. A facula is the location where this energy escapes, making it a little brighter than the rest of the photosphere. Showing people this amazing view occupied me until dinner. I put the scope away because the view was deteriorating as the Sun got lower in the sky and it was clouding up.

The Sun showed another one of its tricks before sunset on Sunday

Me and Rich and the odd annular eclipse graphic on Lowell booth

People started showing up for the astronomer talks that started at 6:00 PM. I set up two demonstrations to coordinate with the Lowell activity booth. One was the spacetime simulator that I use to discuss gravity and General Relativity. I would go through the demos depicted in the viral video plus a couple of new ones. A group from SPS posted a video where they show tides and the Roche limit on this "rubber sheet" model. You toss a group of 4-5 marbles sideways so they orbit the central 2 kg mass that represents Jupiter. They stay in a cluster until they get close, simulating a comet. The curvature of spacetime noticeably increases as they approach Jupiter. The gradient in curvature causes the marbles to stretch out in a line. They get closer, break into individual marbles, and then collide with Jupiter. The point at which they break up is called the Roche limit. I then told the tale of comet Shoemaker-Levy 9. The other additional demo is the simulation of gravity waves. I allude to them earlier when we observe that an orbiting marble spirals into the central mass. This is due to rolling resistance of the marble on the spandex but is a nice analogy for gravity waves. I explain that this effect is not measurable for the Earth orbiting the Sun. That is a relief for those worried the Earth is spiraling into the Sun. I then mention it is measurable for two orbiting neutron stars and the Nobel Prize for physics was awarded to Hulse and Taylor in 1993 for the first measurement of the effect of gravity waves. I first saw gravity waves simulated on a spandex sheet on Steve Mould's video. He mounts 2 castor wheels to a board and then attaches the board to a drill. Place the wheels on the spandex and start the drill. The wheels represent the orbiting black holes. The gravity waves are only visible on a slo-mo video or under a strobe light. I did this demo for my students for the first time last May under a strobe light. The number of "whoas" I heard confirmed my opinion that this was a great demo. Rich brought a drill and generator so we could try it. I showed him how it worked as he took a slo-mo video with his phone. When he watched the video, he exclaimed a loud whoa, just as I expected. Rich was bothered by how the drill and board blocked the view of the orbiting black holes and the point where the gravity waves were emitted. He decided to crawl under the spandex and record a video. His next "whoa" was much louder. His video showed two bumps in the spandex and the waves, but no drill and board. Then we hit on a great idea. Why not have the drill under the spandex? We tried this and knew we had a winner. At the conclusion of my first demo, Rich crawled under the spandex as I instructed the crowd to record a slo-mo video with their phones. After a few seconds of recording, they shared their video with those around them. It was a spectacular conclusion to what I hoped would be a memorable experience. Here is what it looks like:

In between "shows" I would put one or two of the 2 kg masses on the spacetime simulator and let children play with the marbles. That proved to be very popular. Some of them could barely see over the edge but they were fascinated by watching the motion of the marbles. The parents took non-stop pictures. Many people recognized the spacetime simulator from the viral video but they did not recognize me. I told them I was the one in the video and a few people took selfies with me and one even asked for my autograph.

Water refracts light around the edge of the bucket, toward eyes of the observers

Refracted image of the sun was enough to start the cheeping of the osprey chicks

My other demo was a variation on a standard refraction demo. You attach a coin to the bottom of a opaque container. Have students look down on the coin, then move slowly back until the top edge of the container just blocks their view of the coin. Pour water into the container and the coin appears. Have students draw the light path from the coin to the eye for the empty container and the filled container. I decided to super-size this demo so it would work for a larger group. My intent was to make an analogy with the bending of light by refraction with the bending of light by gravity. If the Sun just barely covered a star, you would still see it because the Sun's gravity would bend the light from the star around its edge. The same thing happens at sunrise. The density gradient in the atmosphere bends the Sun's image around the limb of the Earth. When you first see the Sun, it is still below the horizon. In the refraction demo the edge of the container would represent the Sun and the coin would be the star. I thought this was a good analogy to make but was a little concerned that it was too forced. Then I saw this wonderful demo making the same refraction to gravity analogy by Paul Doherty from the Exploratorium. I new if Paul thought it was a good idea, then it really was! To super-size it I used a 5 gallon bucket. Instead of a coin, I wanted to use an LED light. I searched for "waterproof LED" and found many options. It turns out that putting LEDs in the vases of floral arrangements is a thing. I found some that were remote controlled and very bright. I epoxied a washer to the bottom of the light and placed a strong magnet underneath the bottom of the bucket. This prevents it from moving as you pour in the water. As it was getting dark I asked Rich's students from Flagstaff to gather around the bucket. I turned on the "star" and asked them to carefully move back until it was just blocked by the edge of the bucket. I explained the analogy and then started pouring in water. They got excited when the star came into view. I could even see the light hitting their eyes at the moment there was enough water in the bucket. I had a second light that was in the bucket with the water. That allowed me to just keep pouring the water back and forth for each demo. I did this demo a few more times for the people attending the event, then turned the buckets over to the high school students. They quickly mastered the demo, adding their own twists. They liked to ask the crowd to look at the bucket, then they said "imagine there is a star in the bottom" and at that point they would use the remote to turn it on. That got their attention as the bucket had a cool glow to it. Here is a short clip of them doing the demo as seen by an observer:

Rich Krueger's students show gravity bending light

The students also had some cool demos that they helped Rich build. They attached large fiber optic cables to spandex and put a mass on it. This warped the path of the fiber optic cables, showing what gravity does to light. It looked very dramatic at night when they were lit. The students had developed a great presentation. They concluded by showing if the object in the center was a black hole that light would not escape and could be made to orbit it. As I watched the students enthusiastically go through their "show", I thought about the tremendous influence of Paul Doherty who passed away just before the eclipse. Because of Paul I had decided to proceed with the bucket demo and here were some future scientists, engineers, and hopefully teachers, benefiting from his influence. The students had seen Paul's refraction analogy video and had prepared several wineglass bottoms so they could perform it themselves. This is just the tip of the iceberg of Paul's overall influence on every educator and science enthusiast who ever came in contact with Paul or one of his many demonstrations or online posts. The science and education community has lost a giant. However, Paul's influence will continue to resonate and impact many generations to come.

If you are interested in trying the bucket demo I suggest using metal buckets and paint them flat black inside and out so the entire bucket doesn't glow from the light. That will make the desired effect more apparent. Instead of a washer, epoxy a magnet to the light to attach it to the bottom of the bucket. I am sure Paul would have liked this one, I hope you and your students do too.

Rich Keuger takes the audience on a tour of the Universe

As the sky got darker it got cloudier, dampening prospects for the star party and causing anxiety about the next day's total eclipse of the Sun. The forecast predicted it would clear up after 9:00 PM. At about 9:10, half the sky had cleared and by 9:40 it was almost all clear. My faith in meteorologists and their forecasts was restored. Because of the clouds and distance from my van to the football field, I did not set up my 10" SCT. There were some telescopes set up but the main attraction was Rich's telescope connected to a large monitor. Rich would point out where an object was with a green laser pointer, then bring it into view on the screen. He could then describe the object and give details about it to the whole group. He kept a large audience spellbound well after I went to bed.

LGHS AP Physics and APES teachers prepare for totality

I woke up before dawn and watched to see if the osprey chicks started cheeping at sunrise again. They did right on cue. As the sun climbed higher, clouds of smoke became visible toward the southwest. They appeared to be slowly moving toward the region of sky where totality was to occur. As the morning went by, the smoke thinned and became less of an issue. The thin layer of cirrus was more of a concern. I set up the h-alpha again and showed the gathering crowd the chromosphere that would be visible to the naked eye in just a few hours. I was able to leave it tracking the Sun and do a few more shows with the spacetime simulator. The students did more shows and the bucket demo worked great in the daylight too. My sister and her husband arrived from Seattle. One of my colleagues was also there with her husband, 3-year-old son and father. I even ran into a former student who was excited to tell me about his summer internship at JPL. I was disappointed that they did not announce first contact on the PA system. I watched in my h-alpha and listened to the eclipse app someone nearby had countdown from 10. Right at zero I noticed a tiny indentation on the upper right corner. I waited and watched it slowly grow before I announced first contact. Soon after a few sharp-eyed observers could see it in their eclipse glasses. The eclipse I have been waiting for for two decades had begun! I brought out the pinhole picture box I made for the eclipse and it worked great. It shows the equation for General Relativity.

LGHS Teacher with Sun Funnel on 8/21, by R. Peters

In my third post in this series I mentioned using perf board for a pinhole picture. I found it was much easier to punch uniform holes into a piece of cardstock placed on thick cardboard. The pinhole images were crisp if the screen was about 20" from the pinholes. This is a little more than the length of a copy paper box. At this distance the pinhole images won't overlap if they are 4-5 mm apart. A colleague made a DIY video of my design if you want to make one for the next eclipse. They look cool even if there isn't an eclipse! I also mentioned using the Sun Funnel I built. I decided to leave that to my colleagues staying behind at Los Gatos High School. They would have 75% of the Sun covered during the morning tutorial. The big advantage of the Sun Funnel is that it allows many people to safely see the eclipse at once. They also had eclipse glasses and pinhole viewers. My awesome substitute teacher helped with the observing and then streamed totality from Madras on the Exploratorium website, just like my sub did in 1998.

My only good total eclipse picture was still very satisfying

I felt dorky taking a selfie with the eclipsed Sun and the picture captured the feeling

I went to great trouble to bring the large convex mirror I made using a kiddie pool and a spaceblanket that I described in previous posts. When it came time to deploy it, I decided to leave it in the van. All it would show is an all-sky view of the ominous clouds and threatening plumes of wildfire smoke. I also worried it would be a trip hazard. Maybe my next eclipse. I set up my video camera on a tripod and zoomed in on the Sun. I also pointed my GoPro so it would capture some of the crowd and the eclipsed Sun. People were still using my h-alpha to view the partial phase as the clock on the football scoreboard counted down the last minutes before totality. I left it on the tripod and hand-held my camera with the 300 mm telephoto lens. I knew this would smear out the longer exposures but taking pictures wasn't my priority. Time seemed to speed up as the clock counted down. I forgot to ready my binoculars but didn't even realize that until I saw them on the ground after totality. Shadows got sharp, the air cooled, the sunlight seemed to drain from the sky. People were EXCITED! This was really happening. Just before second contact I noticed the contrail of a jet heading toward the Sun. Because the contrail might interfere, I joked that you never have a surface to air missile when you need one. My brother-in-law heard me and took his eclipse glasses off to see the jet. He accidentally got a good look at the slender crescent. We were worried but he seemed fine later. The Science Channel counted down the final 10 seconds over the PA and then BAM, totality. I have seen it before but will never get used to the sight. It looks so wrong and yet so beautiful. I tried tracing the three coronal streamers out as far as I could and looked for structure in the corona close in to the Sun. Coronal structure detail was slightly obscured by the thin cirrus that had plagued us all morning. I don't think anyone witnessing their first eclipse noticed, and if they did, they wouldn't have cared. It was the same amazing life-changing sight I have seen before, and yet was completely unique. I took a quick selfie with my iPhone, then pressed the shutter on my camera and waited for the five bracketed exposures to complete. I looked up at the scoreboard clock and saw only one minute had passed. It seemed like a long time. Now it was prominence time. I saw two very bright ones that revealed their pinkish-red color with averted vision. I was studying these beauties and heard what might have been a warning to prepare for third contact. Before I knew what was happening, there was the diamond ring. I think the countdown clock still had a few seconds on it. Those lunar valleys can be tricky. Some people put their eclipse glasses back on, others just stood there smiling and looking emotionally exhausted. Those that just witnessed their first total eclipse felt compelled to say how unbelievable the sight was. They felt unprepared for what they saw, verifying my belief that there is no way to prepare for this experience. Some had tear tracks down their faces. Before the path of totality swept off the Earth's surface it will have deeply affected millions of people, leaving them with a sense of awe that will not go away.

  Totality starts about 1 min in, focus goes out of whack later but the sound is good!

GoPro of totality with Rush soundtrack. Look for eclipse chasing plane toward lower right.

Sister Colleen, me, and wife Gia, photo by Science Channel

Some people left right away while others stayed for fourth contact and the astronomer talks in the theater. I stayed by my h-alpha and many people stopped by to have a look. They now knew what a prominence really looked like and appreciated being able to see them again. After fourth contact I started packing up. We were ready to leave by about 1:30. We got texts from people reporting heavy traffic but my iPhone traffic map showed it dissipated around Bend with a few slow spots after that. It didn't look like I needed to take my backup route, cutting east over to 395. We headed out, taking a few shortcuts but sticking to 97. That turned out to be a mistake. Something went very wrong in the small town of Chemult about 100 miles south of Madras on 97. Traffic backed up solid from La Pine to Chemult. It took us 10 hours to go about 100 miles. After Chemult there was no traffic but it was getting late. People were pulled over at every turnout, sleeping in their cars. There were no motel vacancies. I was feeling a little tired but considered driving all night. I then realized that would have us arriving in the Bay Area at the peak of rush hour. That would have driven me insane so we found a side road and pulled over for a four-hour nap. Other than the cat that jumped up to sleep on the warm hood of our van, things went smoothly the rest of the way home. When people asked what time we got home, I answered "one hour after totality ended, but on Tuesday!" I have tried finding out what happened in Chemult to no avail. However, I think I know. We have done this drive many times to go skiing at Mt. Bachelor. Chemult is the last chance for gas for many miles while driving south on 97. I think a lot of people stopped at the last gas station and it backed up onto the road. People trying to get back on 97 stopped traffic too. When we drove through Chemult there were a lot of cars at the gas station. The police had coned off the right lane, forcing us to drive in the center turn lane. They would stop traffic going south to let cars back on 97 from the gas station. I think we saw the remnants of what must have been quite a scene. I wonder if the gas station ran out of gas at some point too. I will probably never know for sure but we were both fine with what happened. I had our best substitute teacher for Tuesday and my wife was able to do some business on the road with her phone Tuesday morning. I have often driven that road when there is solid ice, that is worse. I now don't trust the travel time estimates given by my iPhone. During the 11 hours of crawling on 97 it kept saying we were just 8 more hours from home. Had I had better information I would have used my backup route.

I have been looking forward to the 2017 Great American Eclipse for about two decades. Now that it is over I feel a little letdown. The surest cure for post-totality blues is to start planning the next trip to the Moon's umbra. You will probably find me on a cruise ship off the west coast of Mexico in 2024. The 2028 total eclipse in Australia looks good too, I better take care of myself! Although seeing a total eclipse of the Sun is an incredible experience, there are other spectacles of nature that are equally beautiful and inspiring. Seeing an erupting volcano or an aurora come to mind. Perhaps these don't get the same attention because theoretically you can go and see them almost anytime you want, if you can afford it. There seems to be a premium for natural phenomena that are rare. I wonder how people in the future will think of total eclipses when they can board a rocket and travel to the Moon's umbra anytime they want for as long as they want. I believe one of the greatest natural displays, sunsets, are underappreciated because they are ubiquitous. I am glad we don't have to wait years to see one. Usually, all you have to do is take a walk outside and look up.

Sunset, August 20, 2017. If this was rare, I would have a t-shirt saying "I Saw the Great American Sunset in Madras, 2017"