The analemma: why the sun draws a figure eight

Photograph the sun at the same clock time every few days for a year and the images trace a lopsided figure eight in the sky. Its height comes from the tilt of the Earth’s axis, its width and its lopsidedness from the Earth’s elliptical orbit. Here is the analemma over Greenwich, worked out for every day of 2026.

The shape

The analemma over Greenwich

The chart shows where the sun stands at 12:00 Universal Time, Greenwich Mean Time, on every day of 2026, seen from the Royal Observatory in Greenwich.

The analemma over Greenwich: the sun at 12:00 UT on every day of 2026, a figure eight between 15 and 62 degrees high and 4 degrees either side of due south 10° 20° 30° 40° 50° 60° 176° 178° 180° 182° 184° Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec azimuth (south = 180°), stretched four times

The sun at 12:00 UT over Greenwich on every day of 2026. The dots mark the first day of each month. The horizontal scale is stretched four times so the loops can be seen.

Over the year the noon sun climbs from 15.1° above the horizon in late December to 61.9° in late June, while swinging between 176.2° and 184.4° in azimuth, 4° either side of due south. The upper loop, in summer, is narrower than the lower, winter one.

Up and down

The height: the seasons

The vertical extent is the easy part. The Earth’s axis is tilted 23.44° from the perpendicular to its orbit, so over a year the sun’s declination swings from 23.44° north to 23.44° south. At Greenwich that moves the noon sun between 15.1° and 61.9°, a range of 46.9°, twice the tilt. On a planet without tilt the analemma would be squashed into a short horizontal line.

Side to side

The width: the equation of time

If the sun kept perfect time, it would cross the meridian at exactly 12:00 every day and the analemma would be a straight vertical line. It does not: according to the equation of time it runs up to 16 minutes early in November and 14 minutes late in February. At 12:00 GMT the sun is therefore already past the meridian, west of south, in early November, and still short of it, east of south, in February.

Two effects make up the equation of time, and they keep different rhythms. The tilt of the axis makes the sun run early and late twice a year; on its own it would give a symmetrical figure eight with two equal loops. The elliptical orbit makes it run early and late once a year; added to the first, it fattens one loop and thins the other. Together they make the familiar lopsided eight.

The asymmetry

Why the winter loop is bigger

The Earth is closest to the sun in early January and moves fastest along its orbit then. Around that time the eccentricity effect and the tilt effect push the equation of time in the same direction, and the winter loop swells: from November to February the sun at noon wanders 8.2° from east to west, while in the summer loop, from May to August, it stays within 4.5°. The point where the two loops cross falls not on the equinoxes but in mid-April and late August, when the equation of time passes through zero.

Elsewhere

Analemmas around the world, and on Mars

From the equator the analemma stands near the zenith, its loops either side of the overhead point. In the southern hemisphere it appears upside down, with the bigger loop on top, because there the January sun is the summer sun. And it depends on the time you choose: at 9:00 rather than noon the same figure eight leans over to the east.

Other planets draw other shapes. Mars has a more elliptical orbit and a tilt like the Earth’s; its analemma is a teardrop, one loop almost swallowed by the other.

Try it

Photographing the analemma

You need a camera that does not move for a year, a fixed time, and patience. Choose a time on standard time and keep to it through the daylight saving months, or the figure will jump by an hour. Take a frame every week or so, with a strong solar filter for the sun and one ordinary exposure of the landscape, then stack them. The first well-known photograph of the full analemma, by the astronomer Dennis di Cicco, took him through 1978 and 1979.

To see the sun’s position for any time and date without waiting a year, use the sun position map or the sun path diagram.

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