Analemma, O Analemma

Everyone living in the middle latitudes experiences the Earth’s seasons—and people have observed these changes for thousands of years. The sun is highest in the sky during the summer months and lowest in winter.
     Early people weren’t dumb—they could see that as the seasons changed, so did the time of sunrise and sunset. Constructing a sundial to track the daylight hours is an easy matter: put a stick upright in the ground and mark the points that the shadow of the stick’s tip casts in the course of a day.
     Many cultures developed elaborate ways of tracking the annual cycle of the seasons and keeping time, including Sumerians, Egyptians, and Mayans, to name only a few—and these cycles were often based on observations of the Sun, Moon, and sky.
     The term “analemma” was used in Alexandria and Rome for a diagram or “sketch” attributed to the Roman architect Vitruvius. This complex geometrical diagram allowed one to construct a sundial at any latitude without having to make measurements of shadow length. 
     These days, analemma refers to the curve the Sun appears to draw in the sky if its position is captured at the same time of day over the course of an entire year. This curve was difficult to obtain by observation until we developed photographic techniques for multiple exposures.
     The Sun’s position doesn’t trace a straight up-and-down line as it moves through the seasons. Instead, the analemma turns out to be a lopsided figure 8 or infinity symbol. Below is an analemma photographed by Frank Zullo. He took multiple exposures of the Sun at 8:00 a.m. on 37 days spaced throughout a single year. He then superimposed the analemma on a photo of the giant sundial at Carefree, Arizona, to produce this photo. (You can learn more about how he made this photo here.) ​

Photographic analemma superimposed on photo of giant sundial. © Frank Zullo. Used by permission.

The analemma below is a calculated curve that was then superimposed on a photo taken at Croton-on-Hudson, New York. This one is by Daniel Cummings; he used the Stellarium program to plot the curve. (Read more, including how to use Stellarium to make a plot, here.)​

Calculated analemma by Daniel Cummings. © Daniel Cummings, Star in a Star. Used by permission.

The analemma is a result of two characteristics: The tilt of the Earth’s axis (which causes the seasons), and the Earth’s elliptical orbit—it is not a perfect circle. The result is that at some times, the Sun slides ahead of schedule, as measured by a steady, mechanical clock, and at other times, it lags behind. These changes cause the figure 8 pattern.
      If you want to get more technical, see the Equation of Time graph below. “Equation” doesn’t mean a formula in this case, but an “equating” or reconciliation of different characteristics. In this case, apparent solar time (sundial time) is plotted against days of the year. The curve shows the time values ahead of or behind mean solar time (that steady mechanical clock). Above the horizontal line, the sun is ahead, and below, it's behind. The peaks and valleys correspond to the top loop (smaller peak and valley) and bottom loop (larger peak and valley) of the analemma.

Equation of Time. Original by Drini/Zazou, derivative by B. Jankuloski, CC BY-SA 4.0 , via Wikimedia Commons

​I’m thrilled by the analemma because it’s a reminder that the universe contains mystery. Nature doesn’t follow perfectly straight lines, nor does it produce perfect circles or operate only by nice, neat rational numbers—although many cultures have wanted to think so. 

For further exploration
The first photographic analemma was created by Dennis Di Cicco in Watertown, Mass., in 1978 and 1979. You can read about it here. The straight lines in the photo are exposures of the Sun until it reached the time point, to show how it was moving across the sky.

If you're interested in a technical stroll through Vitruvius's diagrams of the traditional analemma, here's a link to an article (you can download a pdf). This article is rather odd, possibly due in part to translation.