Analemma

January 12, 2014

Astronomy

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.
Sundial
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.

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