The Sun's Track Though The Sky

Can you record it, over a year?
Do an animation?

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Flat Earth Academy offers a more general page about finding stuff in the sky over your head. This page concentrates on suggesting a project to learn about the sun's path through the sky.

I've lived many years. And in my experience, the sun has usually... though not always... risen in the east, gone across the sky, and set in the east once every 24 hours.

A challenge

This page isn't so much about answers as about a challenge.

So.. the sun moves across the sky.

Fine. But can we do better?

How quickly does it move across the sky? Does it always move at the same speed? How high is it in the sky in different seasons? In different places?

Of course, everyone has some idea of the answers to these questions. But some people have a very accurate idea.

If you've traveled, you may have noticed that a "sunset" can be quick or slow. Why? How could you put a number on the speed? Why does that matter? Measuring things is at the heart of "science", and science had made our lives easier, given us choices.

How could you "put numbers on" the sun's place in the sky? How could you do it? How would you present the data? And what information could be gleaned from the data?

Who cares? Not everyone. But try this sort of thing a few times, and you may find that you are one of those who actually enjoy taking on such challenges.

I'm not talking about a "trivial" exercise, as in "Where is the sun now?". I'm inviting you to try to design a process for recording where the sun was in the sky across a whole year.

I'm going to suggest an answer which comes in several parts.

Just before we get down to work, I must mention what "inspired" me.

I was visiting the Royal Observatory Greenwich (London), and saw some stunning photos arising from the annual astronomy photography competition.

They weren't all nebulae, and not all required horrendously expensive equipment.

A seven year old with just an iPhone, and, admittedly, a seat in a chartered jet caught a great photo of a solar eclipse. There's more to a photo than the camera. If you'll forgive a slightly mixed metaphor: Would you rather listen to a great pianist playing a $500 piano, or a six year old playing a $5000 piano?

Another photo inspired this page.

Someone set up a pinhole camera, and mounted it very, very firmly to something very immobile where it had a good view of the sky. And for a year, he uncovered the pinhole for a whole day from time to time, on a fairly strict schedule. Can you guess... or find on Google... what his photo looked like at the end of the year?

I am slightly in awe of someone who can put that much work into a single photo! And wait a year to see if he chose film of the right sensitivity.

I've got a way for you to do the equivalent! And you can get friends to help... you won't need to do it all yourself.

At the end of it, you could get a picture like the one from the pinhole camera.

(This page, by the way, is a particularly good candidate, I believe, for the enhancing process I've suggested on my "homework" page.)

The measuring device

First, the instrument. You will have to do the best you can to balance safety, cost, inconvenience, accuracy and precision. But that's what engineers do. And engineering skills aren't irrelevant to "life". Practice with things like sun instruments, which "don't matter"?

Remember the sign in the shop where they repair things: "We can do...

We can do.....

Well done

Pick two.

If it is cheap and fast, it won't be well done... and the other 2 sentences you can put together like that are also true.

Before I continue: DO NOT, for any reason, in particular to pursue this quest, look directly at the sun. Or towards it. The risk is small, if you take some precautions... correctly. But you might make a mistake with the precautions. There is a very real chance of PERMANENT damage to your eyesight.

The tiny risk is too great compared to the huge potential consequences.

That's not just the usual "laywer talk". I mean it.

Outlines of instrument designs

In a perfect world, you could get permission to put up a strong pole, about 2 m high, on a large, horizontal patio. A patio you could mark off with an accurate grid. Or is it more important to make a precise grid? (Both are nice.) What is the difference?

You'd have to site the pole carefully. It needs to go where the top of it's shadow will still be on the patio year 'round. Or you can solve the "too long shadow some days" another way, without compromising your measuring instrument's effectiveness.

Another "answer" would be to have a large hemisphere. Think half a basketball, if a cut basketball would be firm enough to hold its shape. Though bigger would be better. (Why?)

Attach two wires across the "mouth" of the basketball. At right angles to one another.

And mount... so that it will STAY were you've put it, the "basketball" pointing towards where the sun goes, in a place where a shadow from the wires will fall inside the basketball. And mark the insides off with a grid. (Or find a way to be able to put it up/ take it down repeatedly, but always get it put up just as it was before.)

Or use an existing sundial, if there is a good one near you. What is "good"?

Any of the above would do. Each would have pros and cons. "The best" answer is probably something else I haven't listed.

I'm not thinking of anything in particular. Just being humble. There is a completely different approach that I'll mention later. And any of the above, with a little effort to create some image processing software could be the basic of an automatic, electronic instrument capable of taking readings once a minute. (Though probably none would be the basis of even a good automatic instrument.)

(PS: A little while after writing the above, it struck me that all of the above is based on following the progress of part of a gnomen's shadow. A related, but wholly (holey) different approach is also possible, and in fact was the foundation of an experiment which was at the heart of deciding that the earth goes around the sun, rather than vice versa... and the experiment was measuring the sun's position in the sky. (I don't know how positions help answer that question. Maybe you'll know more than me one day. There ARE people who can say how positions help.))

Above all, you need something semi-permanent. Either it can stay where it is all year 'round, or there's a way you can put it back very nearly in the same place, pointing very nearly the same way, the same in many ways, month after month through the year. (You can't put it back exactly, and any differences will degrade your results.

Taking the Reading

Now all you have to do is to take reading!

Write down where the shadow fell at different times, on different dates. Once in a while, track a single day closely, taking readings (using the grid you laid down to "say" where the shadow is lying) every, say, half hour.

This is why this is a project for a group. You don't have to take all those readings. But someone will have to manage things so that no readings are missed. (It isn't just scientists who move science... or any other worthwhile endeavor... forward. Great musicians are important. But few, with the notable exception of one whole class (which?), make their own instruments or print the music that tells Joe Green the tune Bach harmonized nicely.)

Once you have caught your rabbit

Once you have pages of dates/ times/ shadow positions, the fun begins!

And the need for a sub-team with different skills.

It would be relatively "easy"... for those with the skills... to create computer software to turn your readings into an animation of he shadow's behavior. And THAT would be a close analogue of the sun's position in the sky across time. And with a little trig, could be turned into a very good representation of the same. But you're going to be running into the... "inverse"?... of the map-maker's dilemma: How do you show, on something flat, things that are on the surface of a sphere? Because of problems with that, very few people know how big Africa is, or how small Greenland is.

Presenting the data about sun's position in sky is like the mapmaker's dilemma because the best way to present it would be on the inside surface of a huge hemisphere. Not coincidentally, a planetarium would be perfect. (The map-maker can at least make do with a small sphere. Not so the sun path "map" maker, alas.) Given that few homes, schools, museums would want to give up the space to hold such a sphere, a three dimensional problem has to be squashed onto a two dimensional surface.

Once you have the readings, there are many ways the animation could bring the information out of the data.

I am presuming that the software would also do some interpolating between your data points.

They also serve who...

Of course, the readings will quite possibly start life as entries in ink, on paper. Someone is going to have to type a lot of data into a computer. But again... a chore easily conquered by a team.

Cut out the middle man (person)

A fancier "answer" would be less work on a day to day basis. But more work to implement.

It would be entirely possible to build an instrument that pointed something at the sun whenever it was visible. And recorded the turning needed by the supports of the "something" to achieve that. Those measurements of the turning could be... forgive me?... "turned" into a measure of where the sun is in the sky. And it need not be expensive. I could do it for under $80, and most of the "bits" would still be suitable for using for something else, when the project was over.

So... what's keeping you? Are you going to take up the challenge?

Concrete terms

Do what amuses YOU... but if it helps focus your mind, let's say the object of the exercise is a diagram with 12 lines on it, one for each month of the year.

Behind the diagram: A panorama taken outdoors, with a wide enough sweep to have where the sun rises and where it sets when those two events are a far north as the get in the year. That's the horizontal dimension of the panorama.

In the vertical direction, it must go "up" far enough to show where the sun is when it is as high as it ever gets in the year.

Now, on the panorama, your job is to "draw in" a line to show where the sun passes in the sky on 1 January. Put a dot on the line for where it is at 9 o'clock, 10 o'clock, 11, 12... etc. (Make a particularly strong dot for where the sun is at noon... see "Analemma" below.)

And now do it again for the first of February. And March. Etc.

If you've done it right, then another team attempting the same thing, from anywhere on earth at your latitude, will get the same lines.

Before computers, drafting the diagrams would have been a Real Pain. Now... not very hard at all... once you've written the programs.

How you lay out the grid by which you put a number on the sun's position shouldn't matter, as long as you don't change it, or how it is laid out, relative to your gnomen (shadow caster). But do the grid right, and things will be easier for the programmers. What would be best? Why?

If you are undertaking this, you might want to read up on "projections".


A little bonus... the analemma

What do you make of...


I found it, with a useful discussion, in an AboveTopSecret.com blog essay.

You may have seen that "figure 8" before. On a globe or sundial, perhaps.

Before I go further, I need to define "solar noon". Solar noon is the time in the day when the sun is as high as it will get in the sky during that day. This is very hard to determine accurately directly. Can you think how to determine when the moment will be, or (hint) was, indirectly? Your alternative has to allow a more accurate determination to "count".

The photo is what you'd get (with a little work with photo manipulation software to make it "nice") if you took a photo every so often through the year, from a camera which was always set up exactly as before, and if the picture were always taken at exactly solar noon (or a precise time interval to one side or the other of solar noon.)

Sidebar: Oh dear. I was guilty of sloppy thinking. I said "or a precise time interval to one side or the other of solar noon". How do you take a photo an hour before solar noon, when the point of this experiment is to look at differences between solar and "human" noon"? However... you would still get the figure 8 if you took your photo at a precise time after solar noon. It could be an hour, so you would be recording the sun's position at about 1 pm... or it could be 23 hours, if it suited you to record the position a little before the solar noon. (In theory, you'd get a slightly different analemma by each of the methods, I suspect... but I further suspect that they'd all be the same shape, just in a different part of the sky... so you must stick to one "rule" for when you take the photos... or master the mathematics to "move" the sun to where it "would be" at the time you should have taken the photo. (Those mathematics are possible. What would you need?)

There are two things at work here. The sun is higher and lower in the sky at different times in the year... and you can see that in the photo, easily, I think.

But, as well, the sun is a little ahead, and a little behind the human clocks over the course of the year! (Why?!)

But if a day is 24 hours, and if the sun's position defines "a day", how can this be? Did anyone ever claim that from solar noon to solar noon takes EXACTLY 24 hours, every day of the year? (24 hours each of the same length as every other "hour" in the year.) Hmmm. Of course "the day" (the part of the 24 hours with sun) is shorter in the winter than it is in summer. But does the length of a 24 hour day CHANGE over the course of the year? If not, how can the sun be "ahead" (or "behind") where it should be??

Confession: I've thought about these things for a very long time. I never noticed these questions previously. Just shows that it pays to keep thinking. Unless you like being a mindless cow grazing in a field? (We can still ascribe a lack of mental activity to a whole species, if it is cows, I hope? Let me know when one publishes a paper on the sun's movements across the sky.)

Go to Anthony Ayiomamitis's excellent analemma page for more excellent photos and information. Without reading his page too closely, can you think how you would do the photography in order to get the one that has the analemma perpendicular to the horizon? Or maybe the question just shows how little I thought about it, before asking? (I'd seen lots of "tilted" analemmas before seeing the "upright" one.) Why so many tilted ones?

Another instrument concept...

Having written the bulk of what's on this page, I headed to town on errands. Brain still fizzing, as it tends to do in these manic creative bursts.

And yet another instrument design came to mind.

You need a solid, flat, horizontal surface which either won't move, or can be re-established whenever it suits you. ("Re-established" includes that it must be "pointing" the same direction (N/S/E/W) as last time.) With a big "X" drawn on it. Mark one arm "REF". You may or may not want to (try) to make the "X" indicate the four points of the compass, in which case, mark the relevant arm "North". (Magnetic north? True north? And why did I say "try"? Because laying down the X precisely may be difficult. But where-ever you lay it down, leave it here. If, later, you discover that your "north" is 2 degrees east of north, it's no big deal... you can correct your reported data by adjusting how your readings are reported, can't you? I'm not talking about a "fudge", or lying. You just say "My reading was "x", so we know that was "x+2" (or is it "X-2"?)

Back to the new instrument.

You need a hemi-spherical "bowl", or dome of clear plastic. The bigger the better, up to a point. Place it on your flat, horizontal surface, "curve up". Move it about until the all of the line segements between the center of your X and where the lines pass under the edge of the hemisphere. Put marks on the dome at these points, so you can re-place the dome on the X in the same position next time.

Put a grid on the dome, so you can specify any point on it. What grid system makes the best sense for this? How many grid systems can you think of?

Now, using it. I'll describe something crude, first, to give you the idea. Then give you a way to do it better.

Imagine yourself standing beside the dome on the horizontal surface.

Imagine putting your finger somewhere on the dome. A shadow from your finger will fall on the table, won't it?

Now imagine moving your finger about, still on the surface of the dome. At SOME point, the tip of the shadow of your finger will lie on the center of the "X", won't it? Whatever grid lines are under your finger at that point are "the reading" for the sun's position in the sky!

Better than your finger: Make yourself a small... 8cm?... ring with two fine wires, or bits of string, stretched across it.

If you put the ring flat against the dome, an "X" shaped shadow will fall on the surface with the big "X" under the center of the dome, won't it? Slide the ring about until the two "X"s coincide. Take your reading.

Simples! (^_^) (If you can find/ afford the dome, and mark the grid on it accurately. Is it really any better than the more "do-able" designs presented previously? Or... YOU come up with a design... which is better than any of mine!)

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