Why the Sun Draws a Figure 8
Mark the Sun from one location at the same UTC time for 365 days and the dots refuse to form a circle. Earth's 23.4-degree tilt makes the tall loop; changing orbital speed pulls it sideways.
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One camera, one time, one year
Two motions make the analemma
If Earth's orbit were circular and its axis had no tilt, the Sun would return to one point at the same mean solar time each day. The chart separates why the real Sun instead draws an uneven figure eight.
Build a repeatable observation
- Choose the nearest city preset, then move the observer to your location.
- Pick one UTC time that keeps most of the annual path above the horizon.
- Switch to monthly points to preview a practical photo schedule.
- Select dates near the crossing and loop tips, then note altitude and azimuth.
Keep UTC fixed when clocks change
Daylight-saving time can shift a local wall clock by one hour overnight. The Sun does not jump with it. A fixed UTC setting keeps all 365 samples evenly timed. If you are planning photographs by local civil time, convert every date separately and keep the camera position unchanged.
Tilt supplies the north-south motion
Earth's rotation axis leans about 23.45 degrees from the perpendicular to its orbital plane. As Earth travels around the Sun, solar declination moves between roughly 23.4 degrees north in June and 23.4 degrees south in December. That swing controls the vertical reach of the analemma. At Greenwich, latitude 51.48 degrees north, the noon Sun is about 62.0 degrees high near the June solstice and only 15.1 degrees high near the December solstice. Those figures come from the simple noon relation: 90 degrees minus latitude, adjusted by solar declination.
Tilt also affects apparent solar time because the Sun's motion along the slanted ecliptic does not project uniformly onto Earth's equator. Even a circular orbit with the present tilt would produce an east-west timing shift. It would not, however, make the two loops the same shape as the real analemma.
Orbital speed makes the loops unequal
Earth's orbital eccentricity is about 0.0167, small but not zero. The planet moves faster near perihelion in early January and slower near aphelion in early July. Meanwhile our clocks follow a fictional mean Sun that advances uniformly. The difference between apparent solar time and mean solar time is the equation of time. The U.S. Naval Observatory notes that this accumulated difference can reach about 16 minutes. On the chart, that timing error becomes a sideways displacement because four minutes corresponds to about one degree of solar rotation.
Add that displacement to the declination swing and the plotted point crosses itself. The two contributions peak on different dates, so one lobe is wider than the other.
Read the curve from three latitudes
The vertical axis gives altitude from 0 degrees at the horizon to 90 degrees overhead. The horizontal axis gives compass azimuth clockwise from north. At Greenwich the curve stays in the southern sky. Near Singapore at 1.35 degrees north, solar declination passes the observer's latitude twice a year, so the Sun can approach the zenith. In Sydney at 33.87 degrees south, the midday curve faces north and the seasons reverse relative to Europe. Longitude changes which UTC setting puts the curve near local noon.
Data and method
The plot calculates one apparent solar position for every day of 2025 with a compact Jean Meeus approximation. It converts ecliptic longitude and obliquity into solar declination, then combines declination, observer coordinates, and hour angle to get altitude and azimuth. The equation-of-time and daylight readouts use standard approximations. The model omits atmospheric refraction, elevation, terrain, buildings, weather, and the Sun's apparent disk, so check low points on location.
Sources: U.S. Naval Observatory equation of time, NASA reference systems guide, and NASA Earth Fact Sheet.
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Questions about the solar analemma
What causes the Sun's figure-eight path?
Earth's axial tilt moves the Sun north and south through the seasons, while the tilted coordinate system and changing orbital speed shift apparent solar time east and west. Plot both motions together and they form an uneven figure eight.
What does Earth's 23.4-degree tilt contribute?
It supplies the large seasonal change in solar declination, from about 23.4 degrees north to 23.4 degrees south. That change makes the Sun climb and fall on the chart over the year.
What is the equation of time?
It is the difference between apparent solar time, read from the real Sun, and mean solar time, kept by an ideal Sun moving uniformly. The gap varies through the year and can reach about 16 minutes.
Can I photograph an analemma from one location?
Yes, but the camera and framing must stay fixed and every exposure must use the same mean solar time. Use proper solar filtration, account for daylight-saving changes, and expect weather to leave gaps.
Why does the analemma change with latitude?
Latitude changes the Sun's altitude and which part of its daily path is above the horizon. Northern and southern observers face toward opposite halves of the sky, while longitude changes the UTC time of local noon.
The chart uses a fixed UTC time. A real photo series also needs a fixed camera, safe solar filtering, clear weather, and a consistent local clock conversion.