analemma on globe24 hours in a day, 24 beers in a case. Coincidence? Well yeah, maybe. Or maybe not. It probably has something to do with those pesky ancient Babylonians and their obsession with overwrought symbolism. Somehow they got onto a kick about how magical the number 60 is, and how that divides nicely by 12, and then some of the grain stock got wet and smelly, and well I think you can guess the rest. They stayed up all night tasting barley squeezins and thinking up things they could sell cheaper by the dozen, or at least that's what they told their wives.

Eventually the number 12 caught on with the Romans too but let's fast forward to post-Roman pre-Internet days when kids hung out in libraries. There was a humonguagantuan globe. Some of you remember. You would spin it as fast as your tiny hands could make it go and then slow it to a stop with your finger saying "My future spouse is going to be frommmmmmm... UZBEKISTAN!"

Ever notice on the globe there is a strange figure 8? It has tick marks and dates, usually printed somewhere in the middle of the Pacific ocean. It's called the analemma and here is what it is all about. The analemma figure shows which latitude on Earth has the Sun's rays coming vertical (shining straight down) on a given day of the year, and big ass library globes also include the "equation of time" which tells whether local clocks are ahead or behind solar time.

You see the "solar day" is the length of time between one noon, when the Sun crosses your north-south meridian, to the next noon a whole day later. But the length of the solar day is not always 24 hours - its average is 24 hours. That's right, a day is only more-or-less 24 hours. The noon-to-noon time for the Sun can be long or short by as much as about 16 minutes from 24 hours. The "average" rate at which the Sun appears to go around the Earth is what astronomers call "mean time." Not that they are trying to be mean, that's just what they call it, and that's the rate our clocks are based on, our better clocks that is, my watch is kind of moody.


Meanwhile the Earth's axis is tilted which works to move the Sun's relative position north and south during the year, hence the seasons. But the orbit of the Earth around the Sun is slightly elliptical instead of a circle so Spaceship Earth moves faster when it's at perihelion and slower at aphelion, which works to move the position of the Sun slightly east or west of the average position at noon. If the Earth stayed in one place all the time then every noon-to-noon would be the same but since we are flying forward, the length of time it takes to bring the Sun back around depends on how far we moved. And that depends on how fast we traveled.

Imagine swinging a rock around on a string. Let more string out and the rock swings slower, shorten the string and it swings faster. In the Earth's case the difference creates an ever-changing offset between Mean Time (24 hrs) and the appearance of local noon by as much as +/- 16 minutes (approx). The difference between the two is called "the equation of time." You can go ahead and blame Johannes Kepler for most of the math around this one.

The north-south motion of the tilt translates to the height of the figure 8 and all the east-west motion from our changing speed is the width of the figure 8. The top and bottom of the 8 are the solstices and the central crossing point in between is both of the equinoxes. The effects all combine together to make the analemma, which is Latin for weird yearly sun thingy.

Because of the tilt of the Earth and the changing equation of time, if you...

  1. take lots of pictures of the Sun
  2. each from the same location on Earth
  3. always at the same time of day
  4. at intervals for a whole year
  5. all on the same piece of film

This is the sort of image you will get.

analemma photo
photo by Vasilij Rumyantsev

If that's too much trouble try Photoshop. I'm sure the Babylonians would have if they could have.

Carpe Noctem.
Skywise Unlimited

Views: 261

Comment by _Robert_ on January 13, 2014 at 7:31pm

I'm guessing from year to year the trip around the sun varies, so the Analemma shape varies ....? Also; 24 hours is not related physically to a year, thus the need for a leap year to get it to even up again?


Comment by Simon Paynton on January 14, 2014 at 7:41am

That's really cool

Comment by SteveInCO on January 14, 2014 at 10:33am

@Robert.. It doesn't vary, much.  Other planets will have a microscopic effect on our orbit about the sun.

To pick a nit, I don't believe the day to day variation in the length of solar days is 16 minutes, as you stated in the paragraph right before the photograph of the kid serving as the gnomon; rather, that's just the maximum amount solar noon will be off from mean noon, when the sun's position at noon is at the very fattest part of the analemma.  (You did say it correctly in the paragraph with the link to Johannes Kepler.)

A related bit of info:  The actual time the earth takes to rotate around its axis is something like 23 hours and 56 minutes (the sidereal day).  It takes another four minutes (on average) for it to rotate far enough that the sun appears to be in the same place it was a day before, because of the fact that we've moved (on average) a bit less than a degree in our orbit around the sun (360/365.2425 degrees to be more precise)--so the sun appears to have moved that far in the sky.  Thus the earth has to rotate about 361 (360 and 360/365.2425 to be more accurate) degrees for us to see the sun cross the meridian line again.

I said on average, of course because of the earth's elliptical orbit.  As Brad pointed out, the earth will sweep out a bigger (fatter) arc in its orbit when it is closer to the sun, and will cover more than that 360/365.2425th of a degree, and will cover less when it is further away.  It's actually closest about now, so our solar day is longer than its average as the earth has to rotate further to bring the sun onto the meridian line.

In large part I've basically just said what Brad said, in a different way.  When discussing something like this I find it's sometimes helpful to provide two or distinct explanations (since I can't show you a visual model), maybe one of them will make more sense than the other one did, just because it helps the reader form a mental image better for some reason.  Anyhow, I hope one or the other of these explanations was helpful to everyone.


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