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.

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.

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.

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.

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.

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.

 

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.

 

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.

Analemma of Royal Observatory, Greenwich | JPL Horizons