Earth on a dark background with stars and a line through the middle showing the Earth's axis with the marks 23.5 degrees, the Earth's axis, and the equator.

Analemma: The pattern of the sun in the sky

If you took a picture of the sun from the same location at the same time but on different days over the course of one year, what would the pattern in the sky look like? No matter where you are on Earth, the resulting pattern will look like the number 8 in the sky.

This type of chart is called an analema. The purpose of an analemma is to visualize the solar path through time and space as it appears in the sky when viewed from a specific geographic location.

What causes the sun’s position in the sky to change?

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

If the Earth’s orbit were a complete circle and its rotation was perpendicular to the plane of the orbit, we would see the sun appear as a dot that does not move in the sky, no matter what day of the year it is.

The Earth is tilted at an angle of 23.5 degrees. Chart: NASA, public domain.

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

The 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 (perigee) and farther away from it (aphelion).

In terms of time 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.

Illustration with dates showing the change in the Sun's position over the course of a year.  The main image shows a circle of raised stones against a green field and bright blue sky.
Analemma above the Calanish stones showing the changing position of the sun throughout the year with dates (dd/mm). Image used with permission. Image: Credit and Copyright: Giuseppe Petrica,

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 change, true solar time can vary slightly throughout the year due to the tilt of the Earth’s axis and its 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 analema, the equation of time serves as a numerical representation of the east-west elongation of the analema curve. This elongation is a result of the Earth’s elliptical orbit and its varying orbital velocity, which causes the Sun to appear ahead or behind its mean position at different times throughout the year. In charts, the line in the middle represents the meridian. The distance between the analemma curve and this center line represents the difference between true solar time and mean solar time (clock time).

A metal plaque on a gray stone wall with a chart showing the difference between solar time and GMT.
A plaque in Kent showing the year-round variation between true solar time and mean solar time (clock time). Photo: © Ian Taylor And licensed to reuse Under this Creative Commons license.

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. Values ​​range from about +14 minutes to -16 minutes and fluctuate throughout the year. These values ​​are often tabulated or graphed as part of the analemma.

How is an analema chart created?

The word analema comes from the Greek word meaning support. The original purpose of the analemma was to support the basic need for solar timekeeping.

Who created analema?

Jean-Paul Grandjean de Fauci, an 18th-century French astronomer, was the first to introduce the term analema to describe charts showing the Sun’s figure-8 path across the sky over the course of the year at a fixed location and time. Grandjean de Fouchy has been credited by many researchers The analemma was invented in 1830, although some researchers suggest that the German astronomer Johann Philipp von Wurzelbau invented the analemma 15 years earlier..

A pen-and-ink drawing of a globe with markings indicating the path of the sun.
A 1799 pen and ink drawing by John Harris as part of a mathematics thesis. Photo: Harvard University Archives, HUC 8782.514.

Create Analemma

To create an analemma, a person calculates the angle of the sun above the horizon at the same exact time each day and from the same exact location on Earth. The analemma is then created by plotting the position of the sun in the sky or by taking a series of photos from the same place each day and then creating a composite image showing multiple positions of the sun with the background of the sky and landscape remaining the same.

Analemma on globes

Some globes have a figure-8 analema pattern printed on the globe, usually over the Pacific Ocean so that the Earth’s features are not obscured. The purpose is to show the times of the year when the clock is either ahead or behind true solar time.


a tutulemma he Analemma which includes a solar eclipse. The word is a series of analemma and tutulma (the Turkish word for eclipse).

Create an analema for the moon

Photographers used similar techniques to take pictures Analemma moon. The moon returns to its same position in the sky after 50 minutes and 29 seconds every day. The effects of photographing the moon night after night create a similar figure-8 pattern of the moon’s movements in the sky.

An image showing the change in the moon's position over the course of a year.
An analema of the Moon showing the changing position of Earth’s only natural satellite over the course of a year. Image and copyright: Giorgi SuponyaiCC BY-NC 2.0, used with permission of the photographer.


Daniel, C.S.J The Equation of Time: The invention of the analemma, a historical overview of the subject, Part One. Bulletin of the British Solar Society, 1791-100.

Janjoy, A., Lastra, C., and Karasor, F. (2018). In times and shadows: observational analema. Physics teacher, 56(6), 367-369.

Lynch, B. (2012). Equation of time and analema. bull. Irish Mathematics. SOC, 6947-56.



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