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Solar Analemma

A Solar Analemma is a graph or plot that shows the position of the Sun in the sky at a single location and at the same time of the day throughout a year.

Illustration of a solar analemma figure-of-eight above a city skyline
Illustration of a solar analemma figure-of-eight above a city skyline

An oblong figure 8 solar analemma.

If you take a picture of the Sun from the same spot at the same time every day for a year, you will see that it follows the shape of a slightly oblong figure 8, with one loop broader than the other. This is called the Sun’s Analemma curve.

Why Figure 8?

Earth orbits around the Sun on an elliptical path. Earth also revolves around the Sun on a slant; it has an axial tilt of around 23.4 degrees. These two factors combine to generate the figure 8 Analemma curve.

Effect of the Axial Tilt

The 23.4-degree axial tilt of the Earth affects the Sun’s apparent position in the sky – as the year progresses and the Earth continues to spin at a tilted axis and orbit around the Sun, the Sun seems to move up and down (North-South) in the sky. This has the effect of generating the two loops of the figure 8.

The top loop of the figure 8 Analemma is generated during the summer – as the summer months progress, the Sun moves further up on the sky, reaching the highest point around the Summer Solstice.

Following the summer solstice, the apparent position of the Sun starts moving down the sky, generating the first loop of the figure. This effect is repeated similarly during the winter months to generate the second loop of the figure 8 curve.

Effect of Earth’s Eccentricity

If the Earth’s orbital path was elliptical, but its axis not tilted, the Solar Analemma curve would be oval shaped. At the Equator, this line would be a straight line spanning from left to right or West to East.

If the Earth’s orbital path was circular, its axial tilt would have the effect of generating a perfect figure 8 Analemma curve, such that the top and the bottom loop would be the same size. This is however not the case. Not only is the Earth’s orbital path elliptical, the Sun is not in the center of this path. This means that one part of the orbital path (Perihelion) is closer to the Sun than the other (Aphelion).

Because of its orbital shape, the Earth moves faster around the Sun when it is at its Perihelion, around the Winter Solstice, than when it is at its Apehlion. This has the effect of flattening out the bottom half of the curve.

Changes According to Location

In the Northern hemisphere, the Analemma curve has the broader loop at the bottom. This is opposite in the Southern hemisphere, where the broader loop is on the top of the curve.

Observers at the North Pole will see only the top loop of the Analemma, while those at the South Pole will observe only the bottom portion of their Analemma.

In addition, the direction of the Analemma also differs depending on the observers location on Earth,

The Analemma for the Sun has different shapes on each of the 8 planets. This is because the position of the Sun in the sky depends not only on the shape of the planet’s orbit around it, but also on the angle of the planet’s rotational axis.

The term Analemma comes from Greek and refers to the pedestal of a Sundial. Some globes have the Analemma curve printed on the surface.

Plot Your Analemma on the Ground

Follow these simple steps to plot a Solar Analemma using a rod:

  • Find a place where the sun shines at the same time of day all year around.
  • Place a pointed rod in the ground.
  • Every day, at the same time, place another rod to mark the place where the end of the shadow of the first rod is. To simplify things, you can do this on the same date and time each month instead of the same time every day.
  • At the end of the year, you will have a figure 8 plot made by the rods. This is your solar Analemma curve.
  • Instead of using rods, you can mark the shadow point on a large piece of graph paper.

While the time of the day to record the position of the sun can be arbitrarily decided on, there are two things to bear in mind. First, it is important to mark the shadows at the same time each day. Second, account for Daylight Saving Time (DST). If your location observes DST, adjust your marking time accordingly.

Topics: Astronomy, Sun