Understanding the Sun's Figure-8 Curve: The Analemma Explained

Analemma suspended over the city of Athens — A view of the Acropolis and the Parthenon, topped by a perfectly drawn solar analemma in the sky. This asymmetrical tilted "8" figure traces the exact position of the Sun in the sky throughout the year, captured at the same time.
Image source: astronoo.com (new window) — AI-generated image, public domain.

Scientific summary

Astronoo's article explores the solar analemma, the figure-8 curve traced by the Sun in the sky throughout the seasons. It details the two celestial mechanisms behind this curve: the obliquity of the ecliptic (Earth's axial tilt of 23.5°) which generates the vertical movement, and the eccentricity of Earth's orbit which produces the horizontal shift. The article shows how the combination of these effects creates an asymmetrical curve, whose widest branch corresponds to the northern hemisphere winter. It also addresses the practical application of the analemma in correcting sundials and the equation of time.

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

The solar analemma is the figure-eight curve traced by the Sun when its position is photographed at the same time and place every day over a full year. But why this curve and not a straight line? The answer lies in the combination of two fundamental astronomical phenomena: the obliquity of the ecliptic (Earth's axial tilt of 23.5°) and the eccentricity of Earth's orbit. The first phenomenon causes the Sun's height in the sky to vary, creating the vertical component of the 8. The second, related to the elliptical shape of the orbit, changes Earth's speed around the Sun—faster in January (perihelion) and slower in July (aphelion)—generating a horizontal shift. The superposition of these two movements produces this asymmetrical curve, a true celestial signature of the great mechanisms governing our planet. Understanding the analemma means grasping the elegant imperfection of our solar system.

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The analemma: the Sun's figure-8 curve

A fascinating celestial figure

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

Obliquity of the ecliptic: the tilt that creates the seasons

The origin of seasons and vertical movement

Earth's rotation 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.

Eccentricity of Earth's orbit: when the Sun's speed varies

The ellipse and Kepler's law

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

The formation of the 8: when tilt and ellipse meet

The superposition of the two effects

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

Vertical effect (obliquity) : the Sun rises and falls in the sky according to the seasons, drawing the large north-south loop.
Horizontal effect (eccentricity) : variations in orbital speed advance or delay the time when the Sun passes the meridian, causing an east-west shift.

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

Observing and using the analemma: between science and practice

Careful observation

To observe the analemma, one must carry out 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.

A practical application: correcting sundials

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). This is an elegant illustration of the equation of time.

A celestial infinity to understand

The beauty of astronomical imperfection

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

References

FAQ: Everything you need to know about the solar analemma

What is the solar analemma?

The solar analemma is the figure-8 curve traced by the Sun in the sky when its position is observed at the same time and place every day for a full year.

Why does the Sun draw an 8 and not a straight line?

Because two phenomena combine: Earth's axial tilt (23.5°) which makes the Sun rise and fall, and orbital eccentricity which shifts the Sun east or west. Their superposition produces this figure-eight curve.

What is the difference between the vertical and horizontal effects 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 perihelion (early January) and slower at aphelion (early July), which advances or delays the time when the Sun passes the meridian, creating an east-west shift.

Why does the analemma have the shape of an asymmetrical 8?

The asymmetrical 8 shape comes from the combination of the two effects and the fact that perihelion (early January, when Earth is fastest) does not coincide with a solstice. The widest branch of the 8 corresponds to the northern hemisphere winter (December to March), a period when Earth moves faster in its orbit, accentuating the horizontal shift. 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 dial) 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). This is an elegant illustration of what is called the "equation of time".

Can the analemma be observed with the naked eye?

No, the analemma cannot be seen directly with the naked eye. It requires a long-term photograph (a full year) with regular shots at the same time from a fixed point. This image superposition technique then reveals the figure-8 curve.

Is the analemma the same everywhere on Earth?

No, the shape of the analemma varies according to the observer's latitude. In the tropics, the analemma is more upright. Near the poles, it can be almost horizontal. The exact shape depends on the angle from which the Sun is observed.