Suppose you placed a camera at a fixed position, took a picture of the sky at the same time everyday for an entire year and overlayed all of the photos on top of each other. What would the sun look like in that combined image? A stationary dot? A circular path? Neither. Oddly enough, it makes this figure eight pattern, known as the Sun’s analemma, but why? The Earth’s movement creates a few cycles. First of all, it rotates on its axis about once every 24 hours, producing sunrises and sunsets. At the same time, it’s making a much slower cycle, orbiting around the sun approximately every 365 days. But there’s a twist.
Relative to the plane of its orbit, the Earth doesn’t spin with the North Pole pointing straight up. Instead, its axis has a constant tilt of 23.4 degrees. This is known as the Earth’s axial tilt, or obliquity. A 23-degree tilt may not seem important, but it’s the main reason that we experience different seasons. Because the axis remains tilted in the same direction while the Earth makes its annual orbit, there are long periods each year when the northern half of the planet remains tilted toward the Sun while the southern half is tilted away and vice versa, what we experience as summer and winter.
During summer in a given hemisphere, the Sun appears higher in the sky, making the days longer and warmer. Once a year, the Sun’s declination, the angle between the equator and the position on the Earth where the Sun appears directly overhead reaches its maximum. This day is known as the summer solstice, the longest day of the year, and the one day where the Sun appears highest in the sky. So the Earth’s axial tilt partially explains why the Sun changes positions in the sky and the analemma’s length represents the full 46.8 degrees of the sun’s declination throughout the year. But why is it a figure eight and not just a straight line? This is due to another feature of the Earth’s revolution, its orbital eccentricity.
The Earth’s orbit around the Sun is an ellipse, with its distance to the Sun changing at various points. The corresponding change in gravitational force causes the Earth to move fastest in January when it reaches its closest point to the Sun, the perihelion, and the slowest in July when it reaches its farthest point, the aphelion. The Earth’s eccentricity means that solar noon, the time when the Sun is highest in the sky, doesn’t always occur at the same point in the day. So a sundial may be as much as sixteen minutes ahead or fourteen minutes behind a regular clock. In fact, clock time and Sun time only match four times a year.
The analemma’s width represents the extent of this deviation. So how did people know the correct time years ago? For most of human history, going by the Sun’s position was close enough. But during the modern era, the difference between sundials and mechanical clocks became important. The equation of time, introduced by Ptolemy and later refined based on the work of Johannes Kepler, converts between apparent solar time and the mean time we’ve all come to rely on.
Globes even used to have the analemma printed on them to allow people to determine the difference between clock time and solar time based on the day of the year. Just how the analemma appears depends upon where you are. It will be tilted at an angle depending on your latitude or inverted if you’re in the southern hemisphere. And if you’re on another planet, you might find something completely different. Depending on that planet’s orbital eccentricity and axial tilt, the analemma might appear as a tear drop, oval, or even a straight line.