A friend said something about trying to produce his own analemma. That started some musings I enjoyed. This page is an attempt to give you the same fun.
An analemma is a pattern made if you record the position of the sun in the sky by particular rules. I will expand that definition later!
This page is mainly a discussion of things you might consider if you wanted to prove for yourself that what Wikipedia says about analemmas is true.
Where's the fun in just taking some authority's word for something? Can you prove a thing for yourself?... by yourself?.
Why would you care about analemmas? Maybe you never will! But you've watched the sun march across the sky many times. And as it does so, there's a hidden pattern involved. Aren't you just a little curious to see something that has been there all your live, but which you may not have even heard of until recently? Aren't you even just a little bit challenged by "can you do this?" questions>?
Why are analemmas important to the history of humanity's expanding knowledge of the world? Because they tell us things about the pattern of the earth's orbit around the sun.
Here's the structure in the text that follows...
First a bunch of questions which may, superficially, seem daft. Bear with me?
Then more detail about what an analemma is (!)
And FINALLY some thoughts on how you or I might Make Our Own Analemma.
What is a year? What is a day? What are hours/minutes/seconds?
What you mean by any of the above can be different things.
I know a science obsessed person who at seventy years old was still learning what they mean... in some (perhaps obscure) contexts.
Have you really already considered all of the following meanings of the words?
Most 6 year olds can tell you a year is the time between their last birthday and the one that is coming up.
I would guess a six year old would say, though maybe not in these terms, that a "day" is from sunrise to sunset. By that definition the length of a day varies quite considerably, of course. But I believe that in medieval England (and other places), an hour was 12th of the time from sunrise to sunset, and thus also very variable across the year. (The night worked the same way.)
A "day" can be the time from one sunrise to the next. Or maybe from one noon to the next... but what is a "noon"... THAT's not simple, either!
Is an hour 1/24th of the time from a sunrise to a sunrise? Not exactly. And until you know what an hour is, defining minutes as 60ths of an hour, and seconds as 60ths of a minute. Is problematic, isn't it?
And then there are things like "dawn", "sunset", and even "noon". (People who fly planes in the USA have to know about three "twilights"!)
It really is more complicated that we admit it to be in our everyday lives. Happily, unless you have a taste for the arcane, or want to be an astronomer (or run the internet or the GPS system), apart from, maybe, daylight savings adjustments, and leap years, we can get by okay with our "simple" year/ hour, etc, definitions. Whew.
We will need to be careful about what we mean by "day", "hours", "minutes", "seconds" and "noon" if we are going to successfully capture an analemma.
Before I try to address "What is an analemma", I would ask you to think about how "high" in the sky the sun is, summer and winter.
Imagine you could, every ten days though the year, set your camera up in the same place, pointing the same way and take a picture of the sun at noon. (If we don't take the picture at the same time, every day, then how do we know if differences we see between them are not due to the time of day?
Further imagine that you could then "stack" all those images into one multiple exposure.
You'd get a vertical line of dots from the sun in the sky, wouldn't you? The line might be a little wobbly, but the sun is lower in the sky in December than it is in June. If you think about it, you already know that even without all the complicated bits.
An analemma is almost "just" what I just described.
But if you are very, very careful about what you mean by "noon", something extra emerges. Instead of a wobbly line of dots, you get a figure of eight.
(Also, the things that make for an analemma are very slight. You need to be very, very careful that the camera is in the SAME place, pointing the SAME way, every day.)
What is "noon"?
There's a simple definition: Noon is when the sun is exactly (true) south from the observer. Of course, figuring out when that is isn't entirely simple. And even for this simple definition of noon, we need to be careful to use "true" south, not magnetic south. So many ways to go wrong! This would be "solar noon"... I think!
A more complicated definition of solar noon is that it is when the sun is as high in the sky as it is going to get in that day. (I'm sure THIS definition is RIGHT! (^_^))... but again, the concept is simple, but the finding of solar noon in the real world is not trivial... the declination of the sun... it's "height" in sky... changes very slowly around noon. THE moment when it is highEST is very hard to pin down. Sigh.
Another definition... with it's own difficulties is that "noon" today is 24 hours after noon yesterday.
Now we need to know what an "hour" is... not as simple as you might think... and when "noon" was yesterday.
For making an analemma, we want to use the hour that is 1/24th of a "mean solar day".
Did you know that based on solar noon, some days are longer than others?! Although the difference isn't great, the "short" days come in "batches", and the difference between the time by solar noons and by mean solar days can build up to a bit more than a quarter of an hour ahead or behind.
Good news: The GPS system is not only good for finding out where you are, it is also extremely good at telling you very precisely "when" you are! And for our intents and purposes, it tells the time in "mean solar days".
So! If you take a picture of the sun at noon every 24 hours... 24 mean solar day hours... sometimes the sun won't have made it to "due south" yet when you take the picture, and other times it will have gone past due south. The analemma is a diagram of the sun's "poor time keeping"!
Wikipedia (14 Sep 23) says...
The first successful analemma photograph ever made was created in 1978-79 by photographer Dennis di Cicco over Watertown, Massachusetts.
Without moving his camera, he made 44 exposures on a single frame of film, all taken at the same time of day at least a week apart. A foreground image and three long-exposure images were also included in the same frame, bringing the total number of exposures to 48.
(Image is from Wikipedia, where the caption was "Afternoon analemma photo taken in 1998-99 in Murray Hill, New Jersey, USA, by Jack Fishburn. The Bell Laboratories building is in the foreground." Not that this is not Mr. di Cicco's 1979 image.)
The fact that doing this would result in an analemma was well known, years before it was actually done by Mr. di Cicco. the shape it would be was known. But scientists had calculated what it would look like before the actual graphic was created directly from the sun. (You might enjoy trying to figure out why it wasn't done earlier.)
So! "all" we have to do is set up a "camera", take multiple pictures at the same time, and either ensure the camera doesn't move in the course of a year, or devise a way to allow for the fact that it has moved... even if "only a bit".
Lot more could be said on this... but, in a nutshell, as you may have guessed from what has gone before, I would build a system based on repeatedly getting the time from the GPS system. This is neither expensive or difficult. Cost: About $30 (9/32... including a little Arduino to read the GPS receiver and create the "take picture now" signal.). All of the details are in my page about using an Arduino to fetch GPS time.
I would use what is often referred to as an "IP cam". They combine a digital camera with an interface to Wifi or Ethernet interfaces. For an analemma capture, I'd want one with a digital input... i.e. a place where you connect a wire which you will use your GPS receiver/ Arduino to cause a positive edge (transition from "low" to "high") on an output from the Arduino, to "drive" the IP cam to take a picture.
IP cams are often sold as "security" cameras. For our wants, one that takes still photos is sufficient, even though most security cameras are capable of video, of course. Also... we don't need very high resolution. Suitable cameras are sold on eBay and Amazon at modest prices.
The network capability is nice... but not essential. If the images can be "sent" from the camera, it doesn't need to be disturbed to "collect" the images. But, on a tight budget, you might go for a camera that "only" stores it's image to a local memory card.
But... assuming you have a camera which will "send" the picture, where and how will it be sent?
To me, the "cleanest" answer is to set up an FTP server somewhere, let the cameral send the images there. You will have to make sure the FTP server is always standing by each time the image is captured. IP cams can often send images to email addresses, too. "Collecting" the emails, "harvesting" the attachments will be a chore... but so would running an FTP server.
Some cameras, of course, can do BOTH. Maybe go for one of them.
I have to admit that finding "the right" camera, with exactly the mix of functions you need can be a bit frustrating. If you've been to my pages before, you may by now have guessed that I have a page about using IP Cams.
There are also digital cameras you can attach to, say, an Arduino (or Pi), to "make your own" "IP Cam". (A "random" example: The Sparkfun Arducam 5MP Plus OV5642 Mini Camera Module. ($43 + p&p, 9/23)
So far we've spoken of photographing the sun.
This might not be the best way forward.
Pointing delicate sensors, for hours every day, at such a strong light is not a great idea.
And other benefits may arise from "taking the picture" indirectly.
Two approaches have occurred to me...
Establish a flat white surface. Put a grid of lines on it. In the middle of the southern side, fix a very robust stick vertically. Where the shadow from the tip of the stick falls will move with the sun's movements in the sky.
(I haven't developed this idea very fully here... but I hope you can bring your imagination to bear, and flesh out this idea. There's more in this vein in my page about monitoring the sun's position in the sky. (Some earlier material about analemmas is there too. Apologies for the overlap.) I also have another old site with much more, and some of the above better explained.
Again... you're going to have to work a bit to follow this idea. Sorry. I'll try to improve the write up someday.
You would do all of the following on a different scale, but to get the idea across, I'm going to supersize things.
Imagine a box, about 5' on a side. Perhaps a small garden shed. (It has to be robust, and fit to stand outside.
Put it where it will be bathed by the noon-day sun, with one wall facing south.
Seal it up "light tight". Paint most of the inside black.
Make a small hole high in the middle of the south wall.
Now, when you are inside the "box", you can see a "spot" on the north wall (or floor), due to the sun's light coming into the box through the hole.
(Believe it or not, a whole cathedral was once used for just such a "box". What the "spot" did was enormously helpful to scientists trying to prove that the earth goes around the sun, not the sun around the earth.)
Paint the area around where the spot will fall white... and perhaps provide a plane that is more nearly perpendicular to the general direction the sunbeam comes from, paint a grid on the target area, set up a camera to photo the "spot"... and you're done!
Now that you have, I hope, the idea, I further hope that you can re-design the "sensor" to be smaller and less expensive!
What you NEED is to know where the sun is in the sky.
Worth a page or more on its own, but you could make a device to point itself at the sun... and use the inputs needed to achieve that to infer the sun's position!
In a perfect world, a lot of things would be easier.
But it isn't a perfect world.
You will want to take at least one photo (or equivalent) a week of the sun in the sky for at least a whole year... but now that we are in the digital age, there's no particular cost to taking lots more, and if you do you gain options.
You would like to take every picture not only at a particular time... and what that would be is the subject of its own sub-section... but with the same camera, from precisely the same spot, with it facing precisely the same direction.
Oh... and it would be nice if there were no clouds between the camera and the sun.
--- Are you going to bolt the camera to the side of a building? Just set it up once, leave it in place? Consider the problems of thieves and vandals and weather.
--- What can you do...
Make sure there are objects in the image besides the sun. Objects like buildings with nice sharp bits and pieces which you can use to "line up" images which DO show the sun and the building... but with the building in a slightly different position between the two images. It will be a pain in the neck... but it could save you from trying to achieve NO MOVEMENT for another year...!
With some of the more esoteric systems for recording the sun's position, use "vertical" and "horizontal", as determined by a spirit level to your advantage
Take multiple pictures... if you take ONE, at noon, that SHOULD be enough.
If you also take images at 11, 11:15, 11:30, 12:5, 12:30, 12:45, 13:00, you could sometimes "reconstruct" the noon image by interpolation.
This topic has scope for many other analemma-saving ideas!
One way or another, it is likely that you will end up with many individual records of where the sun was at a particular time on a particular date. To turn them into your analemma, you need to merge them all together into a single image. If you used a fancy "Where is the sun? measuring device, you may have a spreadsheet already full of ascentions and declinations. Lucky you!! The work ahead of you is trivial, compared with the task of those who used a less fancy data capture solution, i.e. those who have a set of photos to merge.
In planning how you will do this final step of creating your analemma, remember that you will almost certainly have to introduce compensations for the nuisance of slight shifts of the camera's orientation... the phenomenon you are trying to record isn't huge... you doneed to compensate for those slight disturbances of orientation to get a good result.
You >could, if you have the reference points I spoke of in the "Fixed... or recoverable... camera positioning and orientation" section, tweak the photos "by hand" with a general purpose photo-manipulation package. You'll want to be able to use layers, and have adjustable layer opacity. (I like Gimp, even though it is a bit of a brute. It is open source, free, and multi-platform. And I don't see my needs ever outstripping its capabilities. The early slopes of the learning curve are steep... but... You Can Do It!!) (I will confess that for every day tweaking, cropping, resizing, annotating, color balance adjustments I am not too proud to use the wonderful Irfan Viewer. That and Textpad are two of the principal shackles keeping me... for the moment!... enslaved to Windows.)
Alternatively... especially if you have a big data set (collection of images of the sun in the sky)... you might find that the "image stacking" software used by astronomers would be "the answer" for you. I only know that it exists, and only have a vague idea of what it can do. But, if you have a large data set, at least explore the possibility. The by hand, with Gimp (or similar) approach could be a lot of boring work. If mastering the stacking software proved arduous, at least it might be an interesting challenge. (If you go off searching, adding "comet / asteroid/ supernova finder" to your search might help.) (Comets, etc, are found by repeatedly photographing the same bit of sky and spotting new things in the image. Compensation for shifts in the camera's orientation is probably built in.)
Another approach that will be attractive to a small set of readers, but maybe you are in that set...
Someone with the right skills could write a computer program to scan a batch of photographs and, in each...
That file could be plotted with a spreadsheet program, the result being your analemma!
This page is far from perfect... sorry.
But I hope you found that struggling through it sparked activity in your little gray cells.
I would be DELIGHTED to showcase any analemmas you manage to create, especially if they come with discussions of how you made them. Or to add links to your pages, if you've done an on-line write up.
(See below for contact details)
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