The analemma is an astronomical diagram or curve representing the Sun’s position in the sky as observed from a single location on Earth at the same clock time throughout a full calendar year. This elongated, figure-eight shape arises from the complex dynamics of the Earth’s movement around the Sun. The analemma illustrates the discrepancy between the consistent time kept by mechanical clocks (mean solar time) and the time determined by the actual position of the Sun (apparent solar time). The resulting figure-eight shape is a direct visual consequence of two primary factors: the Earth’s axial tilt and the elliptical nature of its orbit.
Plotting the Analemma: Fixed Time, Changing Position
The analemma is conceptually plotted by tracking two distinct coordinates of the Sun’s apparent position over the course of 365 days. The vertical position of the curve is determined by the Sun’s declination (its angular distance north or south of the celestial equator). The horizontal position is governed by the Equation of Time (EoT), which measures the difference between apparent solar time and mean solar time.
This process involves noting the Sun’s precise location at a consistent, fixed clock time, such as noon, every day of the year. The resulting curve plots the Sun’s changing altitude (vertical movement) and its changing east-west position (horizontal movement). If the Earth’s orbit were perfectly circular and its axis was not tilted, the Sun would appear at the exact same location in the sky every day at the same clock time, resulting in a single point rather than a curve.
The Role of Earth’s Axial Tilt
Earth’s axial tilt, also known as its obliquity, is the primary driver behind the vertical component of the analemma. The Earth’s axis is tilted at approximately 23.4 degrees relative to the plane of its orbit. This constant tilt causes the Sun’s direct rays to fall on different latitudes throughout the year, creating the seasons.
This annual shift in the Sun’s direct rays causes the apparent position of the Sun to move up and down in the sky. The highest point of the analemma corresponds to the summer solstice, when the Sun reaches its maximum northern declination. Conversely, the lowest point corresponds to the winter solstice, when the Sun is at its maximum southern declination. If the Earth had a perfectly circular orbit but still maintained its axial tilt, the analemma would appear as a simple, symmetrical figure-eight, without any horizontal variation.
The Impact of Earth’s Orbital Eccentricity
The characteristic horizontal width and asymmetry of the analemma are caused by the Earth’s orbital eccentricity. Since the Earth’s path around the Sun is not a perfect circle, the distance between the two bodies changes throughout the year. When the Earth is closest to the Sun, at a point called perihelion in early January, it moves faster in its orbit due to gravitational forces.
When the Earth is farthest from the Sun, at aphelion in early July, its orbital speed is at its slowest. This variation in speed means the length of a solar day is not constant. Since the analemma is plotted at a fixed, average clock time, the faster or slower movement of the true Sun causes it to appear slightly east or west of its mean position. This horizontal deviation is precisely what the Equation of Time represents, and it is the combined effect of this horizontal shift and the vertical shift from the axial tilt that forms the recognizable figure-eight.
Analemma Variations and Context
The analemma’s shape is dependent on the specific axial tilt and orbital eccentricity of the body on which it is observed. On Earth, the analemma is a lopsided figure-eight because the largest difference between apparent and mean solar time does not align perfectly with the solstices. For example, the planet Mars has a much more eccentric orbit than Earth, which dominates the effect of its axial tilt.
As a result, the Martian analemma is not a figure-eight but a teardrop shape. Jupiter, on the other hand, has a very small axial tilt of about three degrees, so its analemma is approximately an ellipse, as the effect of its orbital eccentricity is the more noticeable factor. The analemma is often found printed on terrestrial globes and sundials, where it is used to correct the time indicated by the Sun to match the consistent time kept by clocks.