Analemma: The Sun’s Pattern in the Sky

Caitlin Dempsey

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If you were to take a picture of the Sun from the same position and the same time but on different days over the course of one year, what would the pattern look like in the sky? No matter where you are on Earth, the resulting pattern would look like a figure 8 in the sky.

This type of a diagram is called an analemma. The purpose of an analemma is to visualize the solar pathway over time and space as it appears in the sky when viewed from a given geographic location.

What causes the changes in the Sun’s position in the sky?

In very broad terms, the figure-8 pattern of the Sun as it appears to travel across the sky over the course of a year is a result of two factors: Earth’s axial tilt and our planet’s elliptical orbit around the Sun.

If the Earth’s orbit was a perfect circle and its rotation perpendicular to the plane of the orbit, then we would see the Sun appear as a never moving point in the sky, regardless of the day of the year.


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The earth against a dark background with stars and a line through the middle showing the earth's axis with the labels 23.5 degrees, Earth's Axis, and equator.
The Earth is tilted at an angle of 23.5 degrees. Diagram: NASA, public domain.

Instead, the Earth is tilted at an angle of approximately 23.5 degrees relative to its orbital plane which is an eclipse. This tilt is responsible for the occurrence of seasons. It also means that as Earth orbits the Sun, the angle of solar incidence—the angle at which sunlight strikes Earth’s surface—varies throughout the year. This results in a change in the Sun’s declination, or its angular height above the celestial equator.

Earth’s orbit around the Sun forms an ellipse. As the Earth moves in its orbit there are times of the year when the Earth is closer to the Sun (perihelion) and farther away (aphelion).

In terms of time as measured by the position of the Sun, this can vary from day to day. True Solar Time is a method of keeping time based on the actual position of the Sun in the sky as observed from a specific location on Earth.

An annotated image with dates showing the change in the position of the sun over the course of a year.  The main image shows a circle of raised stones against a green field and a bright blue sky.
An analemma over the Callanish Stones showing the changing position of the sun of the course of a year with the dates (dd/mm). Photo used with permission. Photo: Credit & Copyright: Giuseppe Petricca,  gmrphotographer.net/.

For example, local noon occurs when the Sun is at its highest point in the sky for that location. Unlike standard timekeeping which has no daily variation, True Solar Time can vary slightly throughout the year due to Earth’s tilted axis and elliptical orbit around the Sun. The difference between True Solar Time and Mean Solar Time is known as the Equation of Time (ET).

In the context of the analemma, the Equation of Time serves as a numerical representation of the east-west elongation of the analemma curve. This elongation is the result of the Earth’s elliptical orbit and its variable orbital speed, which causes the Sun to appear ahead or behind its mean position at various times throughout the year. On diagrams, a line down the middle represents the meridian line. The distance between the curve of the analemma and this central line represents the difference between between True Solar Time and Mean Solar Time (clock time).

A metal plaque against a gray stone wall with a graph showing the difference between solar and clock time in GMT.
A plaque in Kent showing the variation over the course of a year between True Solar Time and Mean Solar Time (clock time). Photo: © Ian Taylor and licensed for reuse under this Creative Commons Licence.

In essence, the Equation of Time provides the correction needed to convert Mean Solar Time to True Solar Time. In other words, the Equation of Time gives us the number of minutes we need to add or subtract from our clocks to match the Sun’s actual position in the sky. The values range from about +14 minutes to -16 minutes and oscillate over the course of the year. These values are often tabulated or graphed as part of the analemma.

How is an analemma diagram created?

The word analemma comes from the Greek word for support. The original intent of an analemma was to support the primary need for solar time keeping.

Who created the analemma?

Jean-Paul Grandjean de Fouchy, an 18th century French astronomer was the first to introduce the term analemma to describe diagrams that show the figure-8 path of the Sun across the sky over the course of the year at a fixed location and fixed time. Grandjean de Fouchy has been credited by many researchers with the invention of the alamemma in 1830 although some researcher suggest that German astronomer Johann Philipp von Wurzelbau had created the analemma 15 years earlier.

A pen and ink drawing of a globe with marks on it to indicate the path of the sun.
A pen and ink drawing from 1799 by John Harris as part of a math thesis. Image: Harvard University Archives, HUC 8782.514.

Creating an analemma

To create an analemma, a person would calculate the angle that the Sun is above the horizon at the same exact time every day from the same exact position on Earth. The analemma is then created by plotting the position of the Sun in the sky or by taking a series of photographs from the same place every day and then creating a composite photograph which shows multiple sun locations with the background sky and landscape remaining the same.

Analemmas on globes

Some globes will have the figure-8 pattern of an analemma printed on the globe, usually over the Pacific so that land features are not obscured. The purpose of this is to show the times of the year when the clock is either running ahead or behind True Solar Time.

A globe from the early 20th century with a black wire base with a side picture showing an analemma printed on it.
An 8 inche Rand, McNally & Co from 1909. Image: David Rumsey Map Collection, CC BY-NC-SA 3.0.

Tutulemma

A tutulemma is an analemma that includes a solar eclipse. The word is a concatenation of analemma and tutulma (the Turkish word for eclipse).

Creating an analemma of the moon

Photographers have used similar techniques to capture the analemma of the moon. Since the moon returns to the same position in the sky 50 minutes and 29 seconds later each day. The effects of photographing the moon night after night results in a similar figure-8 pattern of the movements of the moon in the sky.

A photograph showing the changing position of the moon over the course of a year.
An analemma of the moon showing the changing position of the Earth’s only natural satellite over the course of a year. Photo and copyright: György Soponyai, CC BY-NC 2.0, used with permission of the photographer.

References

Daniel, C. S. J. The equation of time: The invention of theanalemma, a brief history of the subject, part 1Bulletin of the British sundial society17, 91-100.

Gangui, A., Lastra, C., & Karaseur, F. (2018). On times and shadows: The observational analemma. The Physics Teacher56(6), 367-369.

Lynch, P. (2012). The equation of time and the analemma. Bull. Irish Math. Soc69, 47-56.

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About the author
Caitlin Dempsey
Caitlin Dempsey is the editor of Geography Realm and holds a master's degree in Geography from UCLA as well as a Master of Library and Information Science (MLIS) from SJSU.