Why the Sun Draws a Figure of Eight in the Sky Over a Full Year

Composite astrophotography of the analemma begins with an accident of patience. A photographer leaves the camera fixed, returns at the same clock hour each clear day, and after enough frames the Sun has drawn a tall, asymmetric figure of eight across the sky. The bottom loop is smaller than the top. The crossing point sits closer to the southern end. Nothing about the shape looks like an orbital diagram, yet it is one, a direct portrait of how Earth actually moves rather than how we pretend it moves when we set our clocks.The analemma is the sum of two independent effects that happen to compound across the calendar year.The first is the tilt of Earth's rotational axis, currently sitting at 23.4 degrees relative to the plane of its orbit. Because of this tilt, the Sun appears higher in the sky during one hemisphere's summer and lower during its winter. Photograph it at noon on the June solstice and on the December solstice and you already have two points separated by a large vertical gap. The axis tilt is responsible for the vertical stretch of the figure of eight.The second effect is less intuitive. Earth's orbit around the Sun is not a circle, it is an ellipse, and a measurably lopsided one. Earth reaches its closest point to the Sun, called perihelion, in early January, and its farthest point, called aphelion, in early July. Near perihelion, Earth moves faster along its orbit. Near aphelion, it moves slower. Clock time, however, is perfectly regular: every day is exactly 24 hours by definition. Solar time, the actual moment the Sun crosses the meridian, drifts ahead of or behind the clock depending on where Earth is in its ellipse. This drift is called the equation of time. It is what produces the horizontal wobble in the figure of eight, pulling the Sun left and right of centre as the year progresses.The vertical stretch and the horizontal drift combine into the characteristic asymmetric loop. If Earth's orbit were a perfect circle, the analemma would collapse into a straight vertical line. If the axis had no tilt but the orbit stayed elliptical, it would collapse into a flat horizontal loop. The figure of eight exists because both deformations are present simultaneously and neither cancels the other.The horizontal displacement in the analemma has a practical consequence that pre-industrial timekeepers grappled with for centuries. A sundial reads solar time. A mechanical clock reads mean solar time, the average over the year, smoothed into equal 24-hour days. The two agree on only four dates: around April 15, June 13, September 1, and December 25. On every other day, the Sun is either running fast or running slow relative to the clock by as much as 16 minutes and 23 seconds, which is the maximum difference, occurring in early November.This gap is not a flaw in the sundial. The sundial is correct for the actual Sun. The clock is correct for the averaged, imaginary Sun that moves at perfectly uniform speed along the celestial equator. Astronomers call this imaginary body the mean Sun. Every quartz watch on every wrist is set to the mean Sun's schedule. The analemma is the gap between the two made visible.Astronomical tables that correct for this difference have existed since at least the work of Ptolemy in the second century. The term equation of time itself appears in the work of Christiaan Huygens in the seventeenth century, and by the eighteenth century, quality sundials were being engraved with analemma correction curves so the reader could adjust the shadow reading to clock time without a calculation.Producing an analemma image requires between 20 and 52 exposures over a full year, taken at the same clock hour from the same location with the camera locked to the same framing. Most successful composites use somewhere between 35 and 50 usable frames, since cloud cover eliminates many shooting days. The exposures of the Sun are made on a heavily filtered camera, a dedicated solar filter or a neutral density filter of at least 10 stops, and the background landscape frame is usually taken separately at the same time of day under open sky without the Sun in frame, then composited in post-processing.The resulting image is scientifically accurate. Each dot in the figure of eight is the real position of the solar disc at that hour on that date. The shape will differ slightly depending on the hour chosen: a noon analemma is oriented differently than one shot at 9 a.m. or 3 p.m., because the Sun's path across the sky changes its angle relative to the horizon at different times. The crossing point of the eight shifts accordingly. Photographers in the northern hemisphere shooting at solar noon will see the bottom loop smaller; those in the southern hemisphere will see it inverted.The first widely published analemma photograph is credited to Dennis di Cicco, who completed a composite over the American sky in 1978 to 1979 and published it in Sky and Telescope. Since then, analemma composites have been produced from locations across every continent, and the images from high-latitude sites show a more dramatically elongated shape because the seasonal variation in solar altitude is larger there.The analemma is not unique to Earth, but it is unique in shape to each world. Mars has a teardrop analemma because its orbital eccentricity is much higher than Earth's, about 0.093 compared to Earth's 0.017, and its axial tilt is similar to ours at 25.2 degrees. The high eccentricity dominates, pulling the shape into an asymmetric loop that closes at one end and stays open at the other. Jupiter's analemma is nearly a straight vertical line because its orbital eccentricity is very low and its axial tilt is only 3.1 degrees. On a moon with a tidally locked orbit, the concept breaks down entirely: the Sun barely moves in the sky at all.Calculating the analemma for any planet requires only its orbital eccentricity, its axial tilt, and the angle between perihelion and solstice. Feed those three numbers into the equations and the shape emerges. Earth's figure of eight is a coincidence of its particular values, a different tilt or a more circular orbit and the shape would be unrecognisable.The analemma is a clock, a calendar, and an orbital diagram simultaneously. Every point on it encodes a date, a solar altitude, and a correction factor for every sundial ever built. The figure of eight is not decorative. It is the actual geometry of the year, drawn in sunlight.

Why the Sun Draws a Figure of Eight in the Sky Over a Full Year

More from This Author