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## The Analemma (part 1)

About this time of year, presumably because we are at the Autumn Equinox, photographs of analemmae seem to pop up a lot on the internet and on FaceBook. I showed an example of an analemma to one of my Physics classes last week, and found that they were unable to explain what it shows. So, I figured there was a need for a clear explanation of what a solar analemma shows.

A solar analemma is a photograph taken at the same time each day from the same place, showing where the Sun is in the sky at that same time each day. If one were to take a photo at midday each day, then one would get an analemma that looks like this (bear in mind that one would not adjust when the clocks go forward. So, when they do, one would take the photograph at e.g. 13:00 instead of 12:00 as 12:00 is the real, Solar time).

An analemma taken when it is local noon, hence the “figure 8” is vertical. This analemma must have been taken in the Northern Hemisphere at a latitude between the Tropic of Cancer and the Arctic Circle.

This is the easiest type of analemma to understand, so I will start by explaining this one before we move on to more complex ones. The “figure of 8” you can see in the photograph above is due to two effects. The first is one everyone is familiar with, the changing height of the Sun in the sky in the middle of the day depending on whether it is summer, autumn, winter or spring. The Sun will reach its highest point in the sky at midday in the Summer, but at the same time in the Winter the Sun will be much lower in the sky. This explains the vertical change in the analemma.

On the Spring (or Autumn) Equinox, the Sun at midday is overhead as seen by someone on the Equator. By the time of the Summer Solstice, it will have moved to be overhead at midday for someone at the Tropic of Cancer. On the Winter Solstice, it will be overhead for someone in the Southern Hemisphere on the Tropic of Capricorn. This wonderful picture (taken from here) shows the path of the Sun on the Winter Solstice, the Spring Equinox and the Summer Solstice as seen from Bursa, Turkey.

The path of the Sun on 3 important days as seen from Bursa, Turkey. The top is the Summer Solstice, the middle one is the Spring (or Autumn) Equinox, and the bottom one is the Winter Solstice

But, what about the horizontal change? Why is the Sun sometimes to the left of the vertical midpoint, and why is it sometimes to the right? This is more difficult to explain. It involves something called the Equation of Time, and I will explain it in part 2 of this blog.