Tag Archives: astronomy

573: Apollo 9: Full and Complete

Apollo 9 was the first mission to fly full and complete: Saturn V booster, CSM, LM, and lunar rated spacesuits. They weren’t going to the moon, but they were checking out all the equipment that would take astronauts there.

Jim McDivitt was Commander, David Scott was the Command Module Pilot, and Rusty Schweickart was Lunar Module Pilot. Those designations are a bit misleading. Flying any part of a mission frequently took all hands. It took two people to land on the moon and the Commander was the lead pilot with the Lunar Module Pilot in something like a co-pilot’s role.

This was to be the first flight by a full fledged LM. (By this time NASA had dropped the acronym LEM because the word excursion seemed frivolous, but civilians and the media still called it the LEM.) A LEM mockup had flown unmanned, but the LM that flew on Apollo 9 had been much updated since then.

Apollo 9 lifted off on March 3, 1969 into low earth orbit. The Saturn third stage and attached CSM and LM were then moved into a slightly higher orbit, where the CSM separated, reversed and performed its first docking. The multipart cone which covered the LM was jettisoned at this time. (See 569, and animation in the film Apollo 13). The Saturn V third stage separated at this time and the combined CSM and LM moved away.

The Saturn V third stage had it’s own work to do. It’s engines were fired again to change the orbit’s apogee (high point). Once apogee was reached, the engines fired again to achieve a solar orbit. This firing did not achieve its proper objective, so a third firing took place later. Practically speaking, this merely got the third stage out of the way, but it also gave NASA a chance to once again check the flight characteristics of the Saturn stage which would, on subsequent missions, place the Apollo mission on orbit to the moon.

Aside: if you plan to read more on these subjects you will run into the terms S-IVB, which is the designation for a Saturn V third stage, and SPS, which is the designation for the rocket engine in the Service Module.

Now the CSM was flying backward in orbit attached to the LM, and the LM had opened its struts to a landing stance. The CSM fired it’s rocket for the first time (docking had been done on maneuvering thrusters), raising the orbit and providing the first test for the main engine.

Aside again: this mission should have happened before sending a crew around the moon. Although most of the events of Apollo 9 were firsts, a few things like firing the CSM’s main rocket had already been done on Apollo 8. However, the ability of the linked-up CSM and LM to fly under power had not been tested before.

The next day, the CSM/LM made three more burns, changing orbits and testing the integrity of the CSM/LM connection.

On the third flight day, McDivitt and Schweickart (with backpacks) transferred from the CM to the LM by way of the tunnel between hatches. The day was spent testing out the LM, including a six minute burn of the descent stage engine. McDivitt controlled the last minute manually, throttling up and down and shutting off the engine, just as astronauts would do on a actual moon landing. All this was performed while CSM and LM remained linked-up.

The fourth day of the flight, McDivitt and Schweickart returned to the LM. Schweickart spent thirty-eight minutes testing his spacesuit outside the vehicle. He had also been scheduled to crawl over to the CM to demonstrate how astronauts could be rescued after returning from a moon landing, should the two craft be able to rendezvous, but not dock. Space sickness made this maneuver impossible, but everything in the hardware itself checked out.

On the fifth day of the flight, McDivitt and Schweickart entered the LM for the third and last time, and separated from the CSM.

That is fifty years to the minute before this was supposed to be posted, assuming that my math and data from several different sources were all correct. Great plan, but my internet went down for three days. If fact, this post is coming out about three hours late, but at least I made it before Friday slipped away.

The major test of the LM descent stage engine had already taken place on day three. Now, it fired twice, first to raise the LM’s orbit and then to make it more circular. This was done to separate adequately from the CSM.

The descent stage of the LM was now jettisoned and the ascent stage engine was fired for the first time. This burn moved the LM ascent stage to 75 miles behind and 10 miles below the CSM. Over the next six hours, the LM ascent stage achieved rendezvous and docking. The astronauts moved back into the CSM, and the ascent stage was released. By remote control, it was ordered to fire its engines one last time and burned up in the atmosphere. The descent stage remained in orbit until 1981.

The remainder of the flight was uneventful. The CM splashed down north of Puerto Rico. The SM burned up on reentry, as would all subsequent SMs.

Almost no one remembers Apollo 9. It wasn’t the first Apollo into Earth orbit and it never went near the moon. It was a working astronaut’s flight, one more incremental testing of equipment. But when it was over, everything was ready for the moon landing.

Well, almost everything. There was still the matter of maneuvering the LM downward into a gravity well and out again, and the matter of getting good enough close-up views of the moon’s surface to be sure a landing could be done. Those would be the task of Apollo 10, in May.

One last aside: The April issue of the magazine Astronomy has interviews by the astronauts of Apollo 9. It just came out and I didn’t have time to read it before posting this.


318. Too Many Exoplanets

trappppIt’s official. The good old days are gone.

About a year ago, I said:

(T)he party is nearly over. We now have the capacity to discover extrasolar planets, and new ones are found every year. Fortunately for latecomers to the planet builders guild, megaplanets are easier to find that Earth sized ones, and NASA keeps cutting funding. Still, it won’t be too many years before you can’t decide for yourself where, within the limits of orbital mechanics, you want the planets of Alpha Centauri or Procyon to be.

Science has a way of getting somewhere a lot faster than you would expect. Manned space exploration doesn’t fit that statement, because it runs on politics, not science.

On February 22, in Nature, it was announced that seven Earth size planets had been discovered circling a single star only thirty-nine light years from Earth. Far more important, all seven orbit within the band of temperature where liquid water is a possibility. By contrast, our system has one such planet, Earth, and maybe Mars for a few minutes on a hot afternoon near the equator in mid-summer – if the ice doesn’t sublimate instead. Seven; its unheard of.

The star is TRAPPIST-1, an M dwarf. 

In fact there has been a mini-revolution in the search for exoplanets. NASA’s Kepler space telescope has found more that 4700 potential planets. Many of these will no doubt turn out to be false positives, since the techniques of the search are not perfected, but it is still a staggering number. Most of these were found around stars similar to our sun – where else would you look first? Very few of them are both Earth sized and at the right distance from their star to have the possibility of liquid water.

As I said in Cyan, “planets of no use as real estate.”

Since a mechanical failure in 2013 compromised its ability to orient itself, Kepler has concentrated on observing red dwarfs. To eveyone’s surprise, the planet candidates found around these small, dim stars tend to be more Earth sized. And there are a lot of them.

The TRAPPIST-1 discovery, however, was not by NASA but by the TRAnsiting Planets and Planetesimals Small Telescope group operating out of the University of Liège, Belgium. That explains the use of caps; TRAPPIST is an acronym.

If you want details – and of course you do – the best source is here. This page from the University of Liège is in French, but the video which will self-start is in English, and gives enough details to stir the blood of any space or science fiction fan.

It took me about three seconds to start speculating about what kinds of novels could be written about the exploration of the TRAPPIST-1 system. Suppose most or all of the seven planets had some form of life, all evolving independently. Suppose we write about a paleontological mission on a planet which had vertebral life, then lost it; these dwarfs have a solar wind that operates heavily on planets so close in. Suppose at some time in the deep past, a spacefaring civilization arose on one of these planets, colonized the others, and then died out. Or didn’t die. Or seems to have died until our intrepid explorers begin to poke around.

Okay, I was wrong. The golden age is still here.

220. Planets in Motion

planet story stick 5

Two hundred posts in a little under a year is something of a milestone. What began as an attempt to generate readers for my fiction has almost become a way of life.

I had planned to place this non-writing post as number 200, in celebration, until scheduling issues got in the way. You see, writing a blog isn’t the first activity that I began for the sake of my fiction — which then went on to take over my life. In the early eighties it was clear that I wan’t going to make a living writing novels, and needed a day job. I began working as a substitute teacher to earn some extra money. I was strong, loud, and male so they sent me to middle schools. Substitute teachers don’t like middle school. If you think back a bit, I won’t have to tell you why.

Maybe I’m odd, but I thought the kids were a hoot. I told the dispatcher that I actually liked middle school kids, and suddenly I had full employment. After a year, I went back for my credential (I already had two masters degrees) and got a job at one of the small rural middle schools where I had substituted. I taught there for twenty-seven years, mostly science.

It was an underfunded school and I was a carpenter, so I built a lot of my own science equipment. I shared some of that in posts 201 and 202. A lot of the curriculum sent down from the state was crap, and I was a writer, so I wrote a lot of my own material. I had less hassle from the bosses than most of my friends because good science teachers are hard to find. Ones who aren’t just biding their time, waiting for a chance to move on the high school, are even more rare.

I kept on writing, but at a reduced output. It wasn’t how I had planned my life, but it worked. I once figured out that about 4000 students passed through my classroom during my tenure. I’m proud of that.

Now that I’m retired, I am writing this blog and its sister blog Serial four days a week. Now that’s a day job. This post provides the details about the last big project I built for my science classroom. Pass this on to your science teacher friends.

From this point on, things get technical. If you are a planet geek or a DIY person, you will probably enjoy the details, even if you don’t need the product. Maybe you could make one for your kid’s school?


You can show the scale of the solar system with a model you build yourself (see post 202), but showing how the planetary orbits interact with one another takes some time. I figured out how to do it near the end of my career by building a poster that changed over the course of a school year.

You need a piece of hardboard, 6 ft by 6 ft, 1/8 inch thick, a pint of black or blue-black paint, four tubes of artist’s acrylic (pale gray, blue, green, and red), a one-inch brass drawer pull, four foam daubers, (half inch diameter foam cylinders attached to the end of a dowel, used for laying down stencils), and a measuring device you will have to make yourself.

You find the center of the hardboard poster by running lines from corner to corner; they cross at the center. There you drill a 1/8 inch hole and feed the bolt for the drawer pull from the back. Add a matching nut on the front, tighten, then add a drop of Super Glue to keep things from moving. After you paint the board black or blue-back, spin the drawer pull onto the bolt to represent the sun.

For the four colored circles which will represent the inner planets in their initial position, you will need to go to the website www.theplanetstoday.com. Use the double headed date arrow at the top of the page to chose the date of your initial array. Use the measuring device (building instructions below) to establish each distance from the sun and, referring to the website, make your best visual estimate of where to initially put each planet on its trip around the sun.

At the outset, it won’t look like much, but every week you will add another four dots. By the end of the year Mercury will have circled the sun more than twice, Venus nearly once, Earth about eighty percent of the way, and Mars will have moved a fairly short distance – given the length of a typical school year. I put on new planet circles every Wednesday, since Wednesday almost never has a holiday.

Your students will soon have a clear picture of how the planets move in relationship to each other. When Venus is visible in the west at sunset, or in the east at sunrise, or is not visible at all in the night sky, your wall chart will show them why – assuming that you explain it to them, and keep them at least somewhat excited with assignments like, “What is that red dot in the sky, half way up from the eastern horizon at eight o’clock tonight?”.

The measuring device you will build allows you to place additional planet-circles at the appropriate places for subsequent weeks. It has a single 1/8 inch hole at the left, and eight larger holes. Once a week you will remove the drawer-pull-sun and put the small left hole over the bolt. Place the initial Mercury-hole over the previous week’s Mercury circle and put on a new pale-gray circle into the other Mercury hole, using a dauber. Repeat for all four planets —Mercury pale gray, Venus blue, Earth green, and Mars red. Replace the sun drawer pull and  you are done for the week.

planet story stick 3To build the measuring device, begin with a piece of hardboard 36 inches wide and seven inches high. Draw a line about 1 1/2 inches above the bottom and parallel to it. Clearly mark a point on the line about 1 inch from the left side. This will locate the sun-hole. When all further measurements have been made, an 1/8 hole will be bored at the sun-point and 5/8 inch holes will be drilled at the four pairs of planet-points. Don’t drill anything until all nine holes have been marked accurately.

So far, I have used feet and inches since we have been talking about carpentry. The rest of the dimensions will be in millimeters.

On the base line, measure 215 mm from the sun-point and put a point for Mercury. Continuing on the base line, and still measuring from the sun-point, put a point at 402 mm for Venus, a point at 557 mm for Earth, and a point at 848 mm for Mars.

Each planet needs a second hole, the distance between the two representing the distance the planet moves in one week. For me, these required four radii and four calculated angles. I have simplified (honest, it’s simpler) by giving dimensions above (perpendicular to) the base line, and back toward the sun (parallel to the base line).

For Mercury, this will be 104 mm up and 26 mm back toward the left.
For Venus, this will be 78 mm up and 8 mm back toward the left.
For Earth, this will be 67 mm up and 4 mm back toward the left.
For Mars, this will be 53 mm up and 2 mm back toward the left.

These twin dimensions place the pairs of planet-points at two points on a correctly dimensioned circle, representing the orbit.

Drill the sun hole 1/8 inch to match the bolt holding the drawer pull. Drill the eight planet points 5/8 inch to allow clearance for the 1/2 inch dauber. The outline of the measuring device can be trimmed down to any convenient shape, as long as it encloses all nine holes.

202. Planetary Scale

     Everything in a writer’s life is grist for the mill. For a science fiction writer that includes science itself and, in my case, the teaching of science.
     Here is some more teacher geek. In a book on teaching middle school astronomy, this would be an appendix.

When I was in my early teens and discovered the local library, it not only gave me science fiction, but science as well. I remember the dozen or so books on popular astronomy. I particularly remember How to Build a Telescope, which aroused my lust then dumped me when I found out I didn’t have enough money to but the mirror blanks.

The single issue that most challenged the writers of those books was how to convey the scale of things. Now, if you are under forty, you will have to project your mind back to the days when print technology did not include glossy paper and color photography. Visualize a few grainy black and white photos, a few drawings, and lots and lots of words. Like, “If the distance from the Sun to the Earth were equal to the thickness of a sheet of paper, then the distance to Alpha Centauri . . . “

I grew up figuring out that kind of analogy, but if I gave such a book to one of my modern students, their eyes would glaze over and the wheels would stop turning. The children of Sesame Street have to be shown.

Would you like a simple example? Did you know that a softball is moon-size in comparison to a 12 inch classroom globe of the Earth? And if you hold the softball 30 feet away from the globe, it will be proportional in distance as well as size.

For the rest of the solar system, you can’t show both proportional size and proportional distance in a classroom. You can buy a poster with the proportional sizes, but the planets are all on top of each other. If you make a chart of proportional distances, the individual planets will be too small to see.

You can do both, however, if you are willing to take the exercise outside.

We are about to make a model of the solar system. If you want to get out your calculator, be my guest, but I’ve already done the math and I’m willing to share. The scale I used was one to one billion. It would be easier in metrics, but we will eventually be using a local road map for this, so the good ole American system will have to do.

The chart below is in miles and double-steps. That’s because we want your students to get into the act and count the distance to the planets. A double step is normal walking, counting every time your left foot hits the ground, one-and-two-and-three-and . . .

Your sun will be about five feet in diameter. I looked for years for a balloon that size and never found one, so each year I made a new five foot diameter circle of paper and taped it to the outside wall of my classroom. The distances you need are:

Mercury        38 double steps
Venus            71 double steps
Earth             99 double steps
Mars            150 double steps
Jupiter         513 double steps or 0.5 miles
Saturn                                           0.9 miles
Uranus                                         1.7 miles
Neptune                                       2.7 miles
Pluto                                            3.5 miles

You can skip Pluto if you want, but when I first started doing this, it was still a planet.

Give some of your students models of the planets (we’ll talk about sizes below) and take off with the whole class, counting double steps. At 38, leave the student with the Mercury model and continue with the rest of the class. Et cetera.

My double steps go through Jupiter because our playground allowed us to get almost that far. When we reached the boundary fence, I would tell them, “Jupiter is just beyond that house.” Then I would reel off where Saturn through Pluto would be found. My recital would mean nothing to you; you need to make up your own. Find a large scale local map, measure out distances from your classroom, and memorize them. (For us, Pluto was in the next village.)

None of this would be worthwhile without models to show how small our planets are in comparison to the space they inhabit. I made Mercury, Venus, Earth, Mars, and Pluto out of  beads or glass headed pins, stuck into dowels. Be sure to paint the dowels orange for when Johnny loses one in the long grass. The rest of the planets were made of rubber balls found after multiple trips to toy stores, and painted with artists’ acrylics.

You need these sizes, and this time I’m going metric because it’s way easier.

Mercury       5 mm
Venus        12 mm
Earth         13 mm
Mars           7 mm
Jupiter     143 mm
Saturn     121 mm
Uranus      52 mm
Neptune    50 mm
Pluto            3 mm

Feel free to pass this on to anyone who might want to make this model.

180. Exiled on Stormking

Every science fiction writer has his own style. Mine is built around stories that take place in the near future, in which I try to imagine what would actually happen. Stories of far flung galactic empires or invasions by advanced life forms are certainly legitimate, and I occasionally like to read them. But I write about what I think is most likely to actually happen.

That calls for choices and the most basic is, will or won’t mankind find a practical, artificial immortality. I can’t think of a more basic divergence in fictional timelines. If we do, then events in A Fond Farewell to Dying and its two sequels strike me as entirely logical, even likely.

If not, then we are likely to go on breeding and increasing in population. We are also likely to explore our tiny corner of the galaxy before anyone perfects a faster than light drive. None of our present technologies would allow that. There are a dozen possibilities under consideration, but I am neither impressed nor interested. As I said in 23. Star Drives, it seems more likely that something out there which no one has thought of yet will slap humanity in the face and completely change physics.

You don’t think so? I suggest that you read some of the history of science. Science usually gets things right, but it seems to chase a whole battalion of wild geese first. In the short run, whatever is believed today is likely to be disproved tomorrow. Clinging too tightly to current doctrine is no way to predict the future.

In Cyan, an off stage character named Lassiter discovers that gravity has an inhibiting effect on the conversion of matter to energy. Do I believe that is so? Of course not. I do believe that we are due for a game changer fully as outré as that sometime in the next fifty years. Set your clock.

Cyan, due out momentarily, sets the stage for the exploration of nearby stars at relativistic speeds. While we are exploring Cyan around Procyon, off stage we learn a little about the planetary resources of Alpha Centauri, Sirius, Epsilon Eridani, Tau Ceti. and Epsilon Indi. Call it world building times six, it is a setup for a series of novels.

The first sequel to Cyan, plotted but not yet written, will be called Stormking or Dreamsinger, probably the latter. Stormking is a planet around Sirius A. Perturbation from Sirius B have given it a Uranian tilt, although paleontological evidence shows that this is a relatively recent phenomenon. The human colony lives in space habitats; they are beltmen from Sol’s asteroid belt who have escaped Earth’s destruction. They chose Sirius because Stormking, the only planet in the sweet spot for human life, if basically uninhabitable.

These refugees traveled to Sirius to avoid planetbounds, but during the crowded, decades long journey they had to embrace either fierceness or civility. The former would have killed them, but choosing the latter weakened their spirit.

They no longer tolerate deviations from the norm, yet they are too civil to institute punishment. What choice remains? They send their deviants into exile on Stormking.

Most of them died. A few lived and had children. By the opening of our story, most of the population of Stormking was born there. They have violated no laws, but their rough natures will not allow them to be repatriated.

Antrim, who has been tagged to act as anthropologist and study these children of outlaws, has just arrived on Stormking. He will learn more than he could ever imagine.

171. Solstice Measured

so me

This is a follow on to Monday’s post. If you haven’t read it, you might want to give it a glance.

I’m going to show you how to construct a simple instrument to measure sun angles. It works especially well at the solstice, but a few days late won’t hurt if you are only out to amuse yourself and maybe learn something. I first used this when I was considering where to place windows in a building to get north light without afternoon glare. You could use it to pick out the optimum placement for solar panels, or decide how deep to make a south-facing porch.

FYI to my followers in Brazil, New Zealand, and Australia. I am going to write as if everybody lived in the north latitudes; I’m sure you are used to modifying that kind of writing to meet your own needs. Sorry, but it’s just too clumsy to qualify every statement.

All you need to measure sun angles is a board with a vertical dowel or wire set into it near the center. You could use a carpenter’s square for that. You will need a spirit level to level the board, and it wouldn’t hurt to then use the level to see if the dowel is still vertical (what carpenters call plumb). You will mark the shadows as they fall directly on the board.

This is what I used the second year. The first year i drove a rusty used pipe into the ground and drove stakes into the shadows. Same principle, but far too clumsy.

Next, you need your local sun time. Subtract daylight savings time, but that isn’t enough. Noon, by the sun, is when the sun is directly south of you. Clearly that is an hour earlier on the east side of your time zone than it it on the west side, so you need your longitude and some simple arithmetic.

There are twenty four time zones, each 15 degrees wide. The first time zone is at zero longitude in Greenwich, England but, again, it’s not that simple. Time zones center on their base longitude. The first zone lies from seven and a half degrees east longitude to seven and a half degrees west longitude, and the other zones follow suit. Then all is adjusted to match up with political boundaries, but we can ignore that.

Let’s choose Oklahoma City as a neutral site, so I can give  a shout out to their wonderful Fleming Fellowship, celebrating its sixtieth anniversary this month. OKC is at 97.5 west longitude. If you ignore political gerrymandering, OKC’s time zone centers on 90 degrees longitude, so OKC is on the western boundary of the theoretical time zone; the political time zone ends on the western border of the state. The sun is south of OKC when your watch says 1:30 PM, if your watch is accurate and you have it set for daylight savings time.

To find solar noon for the longitude where you live, add or subtract 3 minutes for every degree you are west or east of the theoretical center of you time zone.

I like to set my board up the day before and rotate it so that the (solar) noon shadow lies parallel to this sides of the board. That isn’t necessary, but it makes for a neater project. Then I’m ready to record the shadow that falls at sunrise.

Sunrise is problematical. You can look it up for your area, but it’s not that simple. (Have I said that before?) If you live on a mountaintop, sunrise will come earlier. If you live in a valley – or, in my case, on the west side of the Sierras – it will come later. How much can’t be calculated. It depends on how far west of that hill you are, and how high that hill is, and whether today’s sunrise happens to fall behind your neighbor’s house, or behind that big oak tree. It will come when it will come. Have a straight edge handy and draw a line from the dowel down the center of its shadow, then write down the time. Continue through the day. I try to make a mark every hour on the (solar) hour.

Early and late shadows will probably run off the board, but for the rest you can calculate the sun’s vertical angle because you will know the height of the dowel and the length of the shadow. Personally, I take the measurements, redraw the triangle on another piece of paper, and measure with a protractor; but then, I grew up before calculators.

You do realize that this is the year’s extreme for north tending sunrise and sunset and for high sun angles, and that every other day until December will be slightly different.

Even if you never design windows for north light without afternoon glare, or plan the placement of solar panels, or decide how deep to make a new porch, taking the sun’s angles throughout the day will give you a better feel for your personal environment, and a new appreciation for the complexities of astronomical observations.

Extreme astronomy geeks will repeat the process at the equinox and winter solstice, but good luck if you try. I’ve never been able to pull off any shadow measurements in December because of clouds.

170. Middle School Astronomy

We learn our astronomy from books, but that isn’t how the science started. The ancient Greeks learned about the stars by looking at the stars. Their understanding was a mixture of observation and myth, with myth sometimes predominating.

When we are young, we also learn astronomy from casual statements we hear from adults. I’ll give you an example. Mars has recently been at a close approach; every evening lately, when I step out my front door (miles from the nearest city) to look at the sky before bed, there it is, red and bright, about halfway to zenith in the south-eastern sky. Now imagine that I say to a child, “Mars is really getting close.” Just that, with no other comment. What images might pop into that child’s mind?


“The seasons change because of changes in the Earth’s tilt.” You might find a statement like that in an old middle school science textbook along with an illustration like this:


Not true. Not a lie, but an oversimplification that may be fine for the average student, but does not do justice to the brightest kid in the room. A better statement would be, “The seasons change because of apparent I changes in the Earth’s tilt”, coupled with an illustration like this:


Now we are more accurate but we’ve confused 90% of the students.

It should be obvious by now that this is a bit of a how-to based on long experience. Even if you aren’t a teacher, you will probably someday have to explain this kind of thing to your own kids.

Let me suggest a third option. First explain things in your best lecture voice with reference to the textbook and with drawings on the board. Then pick a student sitting in the middle of the classroom; out of kindness, choose someone who likes attention. Say, “Helen, don’t move. For the next few minutes, your head is going to be the sun.” Then establish where Polaris lies, for the sake of the demonstration. Your classroom may not allow you to use real north. If some bright, smart-mouth kid catches you out, don’t get mad. Rejoice that someone is paying that much attention and make it a teachable moment.

Now walk around the classroom with the classroom globe tilted toward your Polaris and talk them through the seasons, pointing out that the tilt never changes in relationship to Polaris, but it appears to change in relationship to Helen, our sun. Pat your worst troublemaker on the shoulder as you pass him, wink at the shy girl in the back corner who never volunteers, and say, “Excuse me, Earth coming through,” when you have to dodge around desks.

There is a rule of thumb for teaching science (which probably doesn’t work for algebra). If you enjoy teaching, and you let your students enjoy learning, they probably will.


That exercise was for letting students visualize things they can’t see for themselves. You can also help them see things that happen in their everyday world, but normally go unnoticed.

Observing the path of the sun through the seasons is an Earth’s-eye-view version of the tilted globe carried through the classroom. How do you compress a year’s worth of observation into one 40 minute session, using the real sun instead of charts and graphs? It can be done, but it takes nine observations on your part, spread over three days, with those three days spread over half a year. It also takes a small can of paint and a paintbrush.

When I set this up, I picked a solid, upright, eight foot steel pole which was set up away from the shadows of structures and which I knew would not be disturbed for years to come — a volleyball net pole out on the playground. At 10 AM, noon, and 2 PM (sun time, not daylight savings time) one summer solstice I painted three inch circles (same diameter as the pole) at the pole shadow’s tip.

I repeated those actions during the fall equinox, which was intriguing for my students. I had a paint can and small brush at the ready during my ten and two classes, and on the stroke of the hour, I ran out of the classroom, painted the circle, and ran back in while they watched from the windows. The noon painting had an even bigger audience because of noon recess. As you might guess, I told those who asked questions, “You’ll find out what this is all about — some day.” On Christmas break I painted the last three circles during the winter solstice.

That spring, and for years afterward, I arranged to teach solar motion as near as possible to the spring equinox. The solstices fall outside school days, and the fall equinox is often cloudy in California. I explained everything with lectures, and reading, and drawings on the board, but then we all went out to those nine circles on the playground. As I talked them through the lesson, we all watched the pole’s shadow move. It is fascinating in our mile-a-minute world to take the time to watch a shadow inch its way across the ground. Even if it wasn’t 10 or noon or 2, everyone could see that the shadow’s tip either had or would touch all three of the middle circles.

I explained how I had placed the circles and invited students to lie down with their head on a circle and look past the tip of the pole to see where the sun would be (or would have been) at noon or 10 or 2 on the first day of summer or the first day of winter.

They paid attention. On days they pay attention, learning happens. It isn’t easy, but it works.