Wednesday, July 14, 2004

Drawing The Analemma

What, you might ask, is an analemma?

Take a look at a globe. Somewhere in the Pacific you will probably find an omega (figure-eight) drawn near the Equator. The northern loop of the figure-eight is smaller than the southern loop. This is the analemma. It represents the height of the sun in the sky at different times of year. Why does it have this shape?

We figured this out by covering a table with chart paper. On the chart paper, our instructors had drawn a large circle representing the Earth's orbit, divided into eighths and labeled with dates corresponding to the equinoxes and solstices and dates in-between. We put a MagLight in the center, representing the sun. Then we took a globe and moved it around the circle, observing where the sun was in the sky if observed from the Equator.

I won't go into all the details here. A classroom of 17 science teachers thought about this all morning, and it made all 17 heads hurt. To summarize, the figure-eight shape comes from a combination of factors. First, the Earth is tilted about 23 degrees on its axis. If you hold your globe at an angle and move it around a lightbulb "sun", you'll see that during some parts of the year (summer), the Northern Hemisphere tilts towards the sun, while at other times (winter) it tilts away. This accounts for the sun appearing higher in the sky during the summer than the winter - the vertical part of the analemma.

In addition to the tilt, the Earth's orbit around the sun is slightly elliptical (NOT as much as most textbooks show in diagrams!). During the winter, the Earth is somewhat closer to the sun than during the summer, and is moving faster. This means that at certain times of year, the Earth rotates on its axis slightly farther in one day than it revolves around the sun, while at other times of year, it revolves slightly farther than it rotates. This accounts for the horizontal part of the analemma - sometimes the sun appears to the left of straight up, sometimes to the right.

When you combine these vectors, you get the figure-eight shape.

(Pops a couple of Advil).

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