The Analemma
This is where the Sun stands in the sky at the same clock time every day for a year, as if you photographed it from one spot on every one of those days. The Sun climbs and sinks with the seasons, and it also runs a little early or late against the clock, so instead of a straight line it draws a figure eight. One Sun is drawn each week at its true size, joined by a thread through every day.
| Declination swing | 23.44° north and south |
|---|---|
| Equation of time | 14.2 min late to 16.4 min early |
| Same spot twice, 2026 | 12 April and 30 August |
| Loop sizes | December loop about 6.5 times June's |
What you are looking at
You are standing at the chosen latitude, looking toward the Sun at a fixed time of day, with the horizon along the bottom and the altitude marked up the side. At noon from the northern hemisphere you face south; from the southern hemisphere, north. Each disc is the Sun on one day, one a week, drawn at its real size of about half a degree, coloured cool near the December solstice and warm near the June one.
The top and bottom of the eight are the solstices, when the Sun is highest and lowest at that hour. The crossing in the middle is the one place the Sun visits twice: in 2026 it returns to the same spot on 12 April and 30 August, whatever your latitude or hour. The dotted line at noon is the meridian. On the side marked late, the Sun has not reached it yet when the clock says 12; on the side marked early, it has already passed.
Try a morning or afternoon hour and the eight tilts, because the Sun's daily arc leans across the sky. At high latitudes in winter part of the figure sinks below the horizon, drawn faintly: at that hour the Sun has not yet risen, or has already set.
The math
Two things move the Sun against a steady clock. Up and down is the season: the Earth's axis is tilted 23.44°, so over a year the Sun's declination swings from 23.44° north of the equator to 23.44° south and back. At noon that makes the figure 46.9° tall wherever you stand.
Sideways is the equation of time, the gap between sundial time and clock time. Clocks keep mean time, as if the Sun moved at the same speed all year. It does not, for two reasons. The tilt makes the Sun's eastward motion along the ecliptic count for more or less against the equator at different seasons, and on its own that would draw a neat, symmetric eight. The Earth's orbit is also an ellipse: the Earth moves fastest at perihelion, on 3 January in 2026, and slowest in July, which runs the Sun ahead and behind on a yearly beat. Added together, the Sun runs up to 14.2 minutes late in mid February (11 February in 2026) and up to 16.4 minutes early in early November (3 November).
The eccentric orbit is also why the two loops are so unequal. The loop around the December solstice, when the Earth is near perihelion and the two effects add, is about six and a half times the area of the loop around the June solstice.
How it is computed
For every day of the chosen year the piece asks astronomy-engine, the same library the app's on-device engines use and check against the Swiss Ephemeris, where the Sun is at the chosen hour for an observer at your latitude on the Greenwich meridian. There, local mean solar time is the same as Greenwich time, which keeps the clock exact; at another longitude the same figure appears at the same local mean time. The position is the apparent one, of date, without the bending of light by the atmosphere, which would lift the lowest points by up to half a degree.
The figure is drawn at its true angular shape. The view faces the figure's average direction, across is the angle left or right of that line of sight, and up is the elevation, so the horizon stays straight and nothing is stretched. The equation of time is read from the Sun's hour angle at each sample, the solstices and equinoxes come from astronomy-engine's season search, and the crossing is found where the path's first half meets its second.
Questions
Why is the analemma a figure eight and not a line?
Because the Sun does not keep perfect time. Over a year it runs up to about 14 minutes behind the clock and up to about 16 minutes ahead, so at the same clock time it sits a little east or west of where it would be. That sideways wander, combined with the Sun's seasonal rise and fall, draws the eight.
Why is one loop bigger than the other?
The Earth's orbit is slightly elliptical. Around the December solstice the Earth is near its closest point to the Sun and moving fastest, so the sideways drift adds up quickly and that loop swells. Around the June solstice the effects partly cancel and the loop stays small.
Does the analemma look the same everywhere?
The shape is the same, but where it sits changes. Its height above the horizon depends on your latitude, at noon it hangs due south from the northern hemisphere and due north from the southern, and away from noon it tilts. Near the equator the noon figure passes right overhead.
Can I photograph it?
Yes. Fix a camera in one spot and take a picture at exactly the same clock time every week or so for a year, then combine the frames. Keep to standard time all year, since a daylight saving change would split the figure in two.