Analemma On My Wall

A prism of high quality glass sits in a south window above our mantle. It is part of a surplus optical instrument from WW-II. The window crank gives a sense of its 2″x1″x1″ size.

prism

When the Sun is low in the sky during late fall and winter, light through the prism casts a large full spectrum on the wall on the opposite side of the house. This is a closeup of the spectrum. It is always a delight to see the colors move slowly across the wall during the middle part of a sunny day.

viewspectrum

The Physical Arrangement

To give a better sense of how the prism and walls are oriented I offer these photos. First is a side view taken before the spectrum shines on the opposite wall. The prism sits in the window at the upper left. You can see the spectrum streak on the wall in the living room. About 10 minutes later it projected on a wall in a room out of view to the right.

viewside

This photo was taken from directly in front of the prism window. Notice the spectrum streaked on the left wall in the same place as in the previous photo. In a few minutes it will shine on the distant wall below the light switches.

viewfore

This photo was taken from from the viewpoint of the painting on the opposite wall looking back toward the prism window. Notice the spectrum streaked on the living room wall the same as before.

viewback

About 10 min after the previous photos, the spectrum moved to the opposite wall in the house. From there it slowly moved across the wall to the right as the Sun traveled west across the sky.

viewcolor

 

What About The Analemma?

Over the weeks in late fall approaching the winter solstice, I noticed the spectrum was higher on the wall. The Sun went lower in the sky as we neared the winter solstice. The refracted light of the prism went higher on the wall. In January and February, it reversed the trend and was lower on the wall each passing week.

I documented the location of the spectrum on several days at 11 am starting in late October. Daylight saving time was adjusted. With the passing weeks, we were sometimes blessed with bright sun at 11 am. I set the camera in the same exact location and photographed the wall. The previous photo is from 25 Feb. I was able to record 12 different locations of the spectrum over the weeks.

I later aligned each photograph carefully with Photoshop using the painting and light switches as guides and then superimposed them all. Date labels were attached. What resulted was about half of a typical figure-8 analemma. The link takes you to Google Images for many analemma examples from around the world. Mine is not complete because the spectrum misses the wall during the rest of the year.

analemmaflat

 

What Is An Analemma?

This Wikipedia entry has a good explanation and illustrations. Basically, it is caused by two factors.

The first factor is caused by the axial tilt of Earth. For any specific time of day, the tilt of the Earth changes the vertical altitude of the Sun in the sky throughout the seasons. That explains why my photos showed the spectrum higher and lower on the wall as the weeks went by. Late December put it highest on the wall when the Sun was lowest in the sky due to the refractions and reflections within the prism.

The second factor is caused by the speed of the Earth in orbit around the Sun. Each rotation of Earth brings the Sun around to nearly the same location across the sky for a particular time of day. But, the Earth is also in orbit around the Sun. Where it appears in the sky is affected by our location and speed around the orbit. With each passing day, we travel around the Sun a little farther. We travel about 1/365th of the way around our orbit. The Earth needs to turn a little farther to place the Sun in the same horizontal location as the day before. For example from noon to the next noon as a sundial would see it. If our orbit was a perfect circle, that would amount to almost 4 minutes. Our 24 hour days of 1440 min have that 4 min effect factored in.

Earth does not orbit in a perfect circle. We are closest to the Sun and move fastest during the winter months on either side of the winter solstice. We orbit slowest in the months either side of the summer solstice when we are farthest from the Sun. Those variation in orbital speed effect how far we travel around the Sun each day. They affect whether the Sun reaches noon in 24 hr from the day before. The Sun takes a few minutes longer to reach the noon position in the days either side of the winter solstice.  It is called a slow Sun.

The opposite is true in the days either side of the summer solstice when the Earth is goes more slowly in orbit. Noon is reached early. It is called a fast Sun. The equation of time is rather complex. More detailed explanation can be found at the U.S. Naval Observatory if you are interested.

Astute observers might notice my wall analemma is inverted compared to this one below from the Royal Observatory in Greenwich UK. Their analemma is based on position measurements of the Sun in the sky. My analemma is a projection of the Sun through a prism which inverts the positions. In addition, my analemma does not include any observations between March and early October. It is missing the other half of the figure 8.

Wikipedia Commons | JPL Horizons

Analemma of Royal Observatory, Greenwich | JPL Horizons

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14 thoughts on “Analemma On My Wall

  1. This is a really fascinating record, Jim. Something I hadn’t really thought about in these terms. I’ve focused more on location of the rising sun on the horizon and the position relative to the earth at mid-day through the seasons. I realized a couple years ago that the earth and moon reverse trajectories at the solstices, making their way across the sky through the seasons. It is interesting to ponder!

    Liked by 1 person

    • I had the prism up for a few years and admired the passage of the colors across and up and down the wall. Then it dawned on me to take a picture now and then. I was very pleased with the outcome.

      Thanks for your comments.

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  2. Wonderful post Jim. I have always admired photos that show the movement of Earth around the sun. Unlike many photographic samples, yours relies on the placement on the wall. You could have marked it in pen and made your own calendar. I wonder of ancient people did this? Great job on the alignment. Take care. Bob

    Liked by 1 person

  3. That was an absolute delight! Don’t you just love experiments? I have to admit, I keep my own piece of glass of super low quality so when the sun hits it in the evenings it throws the most beautiful light on the wall. I don’t know how to make it do it or where to sit it to get the most light. Sometimes it works, other times it doesn’t but when I come in the room and see the wall lit up it makes me gasp and smile.

    The glass is dark red. I can’t remember the word. There are several dark colors of red shapes differently w stone between each glass shape.
    Faith

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    • My mother always had a small piece of crystal glass hanging in her kitchen window above the sink. When she died, I got to have it. It now hangs in my window. The sprites of color around the room remind me of her.

      I’m glad you enjoy your special lights. They are good things to have in our lives. They add color and remind us of the cycles of nature.

      Peace to you.

      Like

  4. Beautiful Jim. Interesting how they call them Analemmas, it’s like the pattern.

    I meant to share these with you. It’s in the Wiki article of “equinox”, but I liked the illustrations, I hope the link works. It is a slideshow. It has to do more with the sun’s arc as seen from the equator and how the shadows become more enlongated.

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