The analemma: why the Sun traces a figure of eight

How the figure of eight forms

Imagine making repeated solar photographs from the same fixed viewpoint, always at the same standard-time reading and without a daylight-saving change. On a circular Earth orbit with an upright rotation axis, the Sun would return to the same point. On the real Earth, two changes combine.

• **Declination changes vertically.** Around the June solstice the Sun is about 23.4° north of the celestial equator; around the December solstice it is about 23.4° south. The annual declination range is therefore nearly 47°.
• **The equation of time changes the sideways position.** The Sun sometimes reaches the meridian ahead of mean solar time and sometimes behind it. This displacement is much smaller than the north–south annual range, giving a narrow figure rather than a broad loop.

Together they produce the crossing curves of the eight. The analemma connects the same two quantities represented in a plot of solar declination against the equation of time. Its appearance in a local photograph also depends on how those celestial directions project onto your horizon and camera frame.

What the shape tells you

The two loops are unequal. Earth’s elliptical orbit makes it move faster near perihelion in early January. Its effect combines with axial tilt differently in different parts of the year, enlarging one loop relative to the other. Calling this the “winter loop” without a hemisphere would be misleading: the larger loop belongs to the northern winter half of the year, which is southern summer.

The daily positions are unevenly spaced. Near the solstices, declination changes slowly, so adjacent dates crowd near the ends of the figure. Around the equinoxes, it changes much more quickly, spreading the points farther apart through the middle region.

The crossing does not mark the equinoxes. It represents two dates with matching declination and equation-of-time values, approximately in April and late August. The exact dates are not a shortcut to an equinox prediction.

Other planets would produce different analemmas because their axial tilt, orbital eccentricity and perihelion geometry differ. Earth’s shape is a signature of its own orbit. On older terrestrial globes, an analemma printed over an ocean served as a reference chart for solar declination and the equation of time rather than depicting a physical feature of that ocean.

Your viewpoint changes the orientation. At middle northern latitudes near noon, the figure stands in the southern sky. At middle southern latitudes it appears towards the north with a different orientation; tropical views can pass across the zenith. Morning and afternoon figures are tilted relative to a noon view.

Sundials and the history of the analemma

The pattern was understood long before it could be photographed. Some sundials place a figure of eight beside the noon line so that the date-dependent solar position can be related to mean solar noon. Meridian lines in buildings can use a small aperture to cast a moving spot of sunlight onto a marked floor.

A celebrated early photographic example was Dennis di Cicco’s year-long analemma project in the United States in 1978–1979, made through repeated exposures on one piece of film. Modern digital compositing makes the recording more flexible, but the essential discipline is unchanged: consistent location, orientation and time.

Photographing an analemma yourself

1. Fix the viewpoint. Keep the camera position and direction identical throughout the project. Mark a stable position and framing so that moving a tripod does not change the geometry between sessions.
2. Use a consistent time basis. Follow the same standard or mean-clock reference all year. If your civil clock moves forward for daylight saving, the corresponding displayed time also moves forward; continuing at the same displayed hour would create displaced pieces of curve.
3. Use appropriate solar filtration. Solar exposures require a purpose-built filter securely fitted over the front of the lens. Never look through an unfiltered optical viewfinder at the Sun.
4. Choose a workable cadence. A photograph about every seven to ten days can reveal the figure. Nearby clear days can fill gaps caused by clouds without pretending that the weather follows a schedule.
5. Plan the foreground separately. A landscape exposure can be combined with filtered solar images afterwards, with camera and solar-safety precautions appropriate to each exposure.

The chosen time sets the location and tilt of the figure in your composition. A New York balcony project and an Arizona landscape project require different framing even if their cameras follow the same standard-time rule. Starting near a solstice gives you slower daily position changes while you test framing and exposure.