The analemma is a celestial concept representing the path the Sun appears to trace in the sky over the course of a full year. This path is only visible if an observer records the Sun’s position at the exact same clock time each day from a fixed location. The resulting shape is a complex, elongated curve that is fundamental to understanding the difference between solar time and the standardized time kept by our clocks.
The Figure-Eight Shape
The most recognizable feature of the analemma is its distinct figure-eight shape. This pattern is a visual plot of two specific astronomical coordinates. The vertical axis of the figure-eight represents the Sun’s declination, which is its angular distance north or south of the celestial equator. The horizontal axis represents the Equation of Time, which measures the difference between the Sun’s actual position and its average position.
The figure-eight shape is generally taller than it is wide, spanning approximately 47 degrees vertically on the celestial sphere, which is twice the Earth’s axial tilt. The highest and lowest points of the analemma correspond to the summer and winter solstices, respectively. The two points where the loops of the figure-eight cross mark the vernal and autumnal equinoxes, where the Sun’s declination is zero.
The shape itself is not perfectly symmetrical; one loop, typically the northern one, is often smaller than the other. Plotting the Sun’s position requires consistent observation over 365 days to fully capture this complex, closed curve.
Two Causes of the Analemma
The figure-eight form of the analemma results from the superposition of two independent astronomical motions of the Earth. The primary cause is the axial tilt, or obliquity, of the Earth’s rotation axis, inclined about 23.4 degrees relative to its orbital plane. This tilt is responsible for the seasons and creates the entire vertical spread of the analemma, causing the Sun to appear to move north and south in the sky throughout the year.
The axial tilt also contributes significantly to the horizontal component of the analemma. When the Sun is near the solstices, its apparent movement along the ecliptic translates less into east-west change and more into north-south change. Conversely, near the equinoxes, the same movement along the ecliptic causes a larger apparent east-west shift, creating the twice-yearly horizontal wobble that forms the figure-eight loops. If the Earth had a perfectly circular orbit but maintained its axial tilt, the resulting analemma would be a perfectly symmetrical figure-eight.
The second cause is the Earth’s orbital eccentricity, meaning the orbit around the Sun is an ellipse, not a perfect circle. According to Kepler’s Second Law of Planetary Motion, the Earth moves fastest when it is closest to the Sun, at perihelion in early January, and slowest when it is farthest away, at aphelion in early July. This variation in orbital speed causes the Sun’s apparent motion to speed up and slow down relative to a steady, clock-based average. This difference in speed creates the horizontal displacement and is responsible for the noticeable asymmetry between the northern and southern loops of the analemma.
Analemma and the Equation of Time
The analemma is fundamentally a graphical representation of the Equation of Time (EOT), which is the calculated difference between two ways of measuring solar time. Apparent Solar Time is the time indicated by the actual position of the Sun (like on a sundial), and Mean Solar Time is the uniform time kept by mechanical clocks, based on the average length of a solar day.
The EOT is the precise measure of this discrepancy, showing how much “ahead” or “behind” the actual Sun is compared to the clock’s average Sun. This difference is plotted along the horizontal axis of the analemma, with the curve extending a maximum of about 16 minutes fast in early November and about 14 minutes slow in mid-February. The EOT is zero only four times a year, when the apparent and mean solar times align:
- April 15
- June 14
- September 1
- December 25
This variation means that the moment of solar noon—when the Sun is at its highest point—does not occur at exactly 12:00 P.M. clock time every day. The analemma illustrates this annual cycle of time correction, which was historically important for mariners and astronomers.
Depicting the Analemma
The analemma has historically been depicted on various instruments and objects as a practical aid. Many terrestrial globes feature the figure-eight printed onto the Pacific Ocean, often near the 180-degree longitude line. On these globes, the analemma serves a dual purpose, showing both the Sun’s declination for any given date and the corresponding Equation of Time. The vertical position indicates the latitude where the Sun is directly overhead at noon on a specific day of the year.
The concept of the analemma is also applied to sundial design to improve accuracy. A standard sundial indicates Apparent Solar Time, which deviates from Mean Solar Time by up to 16 minutes. To correct this, some sophisticated sundials incorporate an analemma curve directly onto the dial plate or use a specially shaped gnomon, the shadow-casting element, to automatically compensate for the Equation of Time.
In modern times, the analemma is most dramatically observed through a specific type of long-exposure photography. This process involves taking a photograph of the Sun from the exact same location and at the same clock time throughout the entire year. When all the solar images are composited onto a single frame, the final image reveals the figure-eight path of the Sun suspended over the landscape.