The Analemma: When the Sun Draws a Figure 8 in the Sky

What is the solar analemma and why does the Sun draw a figure 8 in the sky?

The analemma is the figure-eight shape that the Sun traces when its position is photographed at the same time and place every day for a full year. This curve results from the combination of two fundamental astronomical phenomena: the obliquity of the ecliptic (the 23.5° tilt of Earth's axis, which varies the Sun's height and generates the vertical component of the 8) and the eccentricity of Earth's orbit (which makes Earth faster at perihelion in January and slower at aphelion in July, creating a horizontal offset).

The Analemma: The Sun's Figure 8 Curve

The solar analemma is the figure-eight shape that the Sun traces when its position is photographed at the same time and place every day for a full year. This curve results from the combination of two fundamental astronomical phenomena: the obliquity of the ecliptic (the tilt of Earth's axis) and the eccentricity of Earth's orbit.

The Obliquity of the Ecliptic: The Tilt That Creates the Seasons

Earth's rotational axis is tilted by about 23.5 degrees relative to the plane of its orbit around the Sun. This obliquity is the origin of the seasons. It directly influences the height of the Sun in the sky over the months. Thus, the Sun's declination varies between +23.5° at the summer solstice and -23.5° at the winter solstice, generating the vertical component of the analemma.

The Eccentricity of Earth's Orbit: When the Sun's Speed Varies

Earth's orbit is not a perfect circle but a slightly flattened ellipse (eccentricity of about 0.0167). As a result, the Earth-Sun distance varies throughout the year. According to Kepler's second law, Earth moves faster at its perihelion (early January) and slower at its aphelion (early July). This uneven speed modifies the duration of the apparent solar day, thus creating a horizontal offset in the analemma.

The Formation of the 8: When Tilt and Ellipse Meet

The characteristic figure-eight shape of the analemma arises from the superposition of the two previous effects:

The asymmetry of the two loops of the 8 is explained by the fact that the perihelion does not coincide with a solstice: the wider branch corresponds to the northern winter (when Earth moves faster).

Observing and Using the Analemma: Between Science and Practice

To observe the analemma, you must take a photographic exposure spread over a year: a regular shot at a fixed time from a fixed point. This meticulous work reveals the complex dance of the Sun over the days.

The analemma also has a practical application: it allows the correction of sundials to convert from apparent solar time (irregular) to mean solar time (regular). It is an elegant illustration of the equation of time.

Conclusion: A Celestial Infinity to Understand

The solar analemma is much more than a beautiful curve. It is a synthetic graphical representation of Earth's major movements: rotation, axial tilt, and elliptical revolution. Understanding it means grasping an essential aspect of celestial mechanics and discovering, in the apparent regularity of the sky, an elegant imperfection that makes all the beauty of our astronomy.

FAQ: Everything You Need to Know About the Solar Analemma

What is the difference between the vertical effect and the horizontal effect that form the analemma?

The vertical effect is due to the obliquity of the ecliptic (Earth's axial tilt of 23.5°). It causes the Sun's declination to vary between +23.5° at the summer solstice and -23.5° at the winter solstice, generating the north-south movement of the Sun in the sky. The horizontal effect is due to the eccentricity of Earth's orbit (ellipse). According to Kepler's second law, Earth moves faster at its perihelion (early January) and slower at its aphelion (early July), which advances or delays the time when the Sun passes the meridian, creating an east-west offset.

Why is the analemma shaped like an asymmetrical 8?

The asymmetrical figure-8 shape comes from the combination of the two effects and the fact that the perihelion (early January, when Earth is fastest) does not coincide with a solstice. The wider branch of the 8 corresponds to the northern winter (December to March), a period when Earth moves faster in its orbit, which accentuates the horizontal offset. In summer, Earth is farther away (aphelion) and moves more slowly, making the corresponding loop narrower.

What is the practical use of the analemma?

The analemma has a direct practical application: it allows the correction of sundials. Indeed, apparent solar time (read on a sundial) is not regular throughout the year due to orbital variations. The analemma provides the correction to apply to convert to mean solar time (the time on our watches). It is an elegant illustration of what is called the "equation of time".