Sunday, December 28, 2008

What's that analemma for, anyway?

If you're lucky, you live in a house with an analemma.

It's not a pet, but an interesting feature printed on certain globes. It looks like a stretched out figure eight, and is where the sun would be in the sky if you took a photo of it at the same time every day for a year.

Those who live on the equator would see the sun move east and west, while someone at the North Pole...What would he see?

Believe it or not, the sun does trace this stretched out 8.

 The sun is at its lowest point in the 8 on or around the winter solstice and at the top of the 8 on the summer solstice. (In the Southern hemisphere the analemma is upside down.)

Two factors produce this oddity. The first is that Earth is tilted at about 25.4 degrees to the plane of its orbit.  That accounts for the east to west to east to west movement. The north to south apparent motion is a consequence of the Earth's orbit.

This should not come as a surprise, but the orbit it an ellipse.  Consequently, the planet speeds up when it is nearest the sun, in January, and slows down when it's farthest away, in July.  The difference in speeds is confounding, because our clocks are designed as if the orbit were a circle. 

Practically, this means that your watch is ahead for six months and then behind for six months,
compared to where the sun should be in the sky. This difference is called the Equation of Time. We never hear about this for some mysterious reason. We just keep following our watches and clocks, and let the sun do its own thing. 

What if you want to construct your own analemma? You could do it with a stationary camera, but it gets complicated. Either all of the exposures must be on one piece of film, or all of the frames must be assembled and superimposed at the end. 

Or, make one of those contraptions for viewing solar eclipses: a box with a pinhole at one end and a piece of paper at the opposite end. Now, all you have to to is keep the box in the exact same spot for a year, and at the same time every day, look inside, see where the sun is projected on the paper, and put a dot there. 

After a year, you should have an elongated figure eight shape. This still leaves some questions. For starters, the sun is obscured by clouds on many days in New England. More puzzling, is what does "the exact same time" mean?  

Given the Equation of Time business, should we use the actual "sun time" or our oscillating piece of quartz time?  Perhaps you could make two sets of dots, one for solar time, the other for man-made time. 

Also, since the box is going to be outside for a year, use something durable. Do not use cardboard.

Finally, you may have to explain to a neighbor or two what you're doing. If he or she asks why you're outside with your head in a box, just say, "I'm looking for my analemma."

Pretty soon everyone will leave you alone.

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