How does the analemma relate to the motion of the sun along the ecliptic?

Answer 1

The Sun is always on the ecliptic, even though the analemma seems to suggest that the Sun is engaged in some kind of fancy wobble.

The analemma has a "figure of eight" shape. There are two components that cause this shape.

First, the Sun seems to move in the north-south direction in the sky during the year, because of Earth's tilted axis.

The second component is explained below. This is about the Sun's apparent daily motion East to West across the sky:

The analemma is also caused because civil time or Universal Time (UTC) does not line up perfectly with "apparent solar time". Apparent solar time is what a sundial measures. UTC is almost exactly the same as "mean solar time" (the original "Greenwich Mean Time"). Our clocks are based on UTC.

UTC gives the average day length over the course of a year, independent

of the exact position of the Sun in the sky.

The difference between these two measurements of time is caused by the Earth's tilt (again) and the Earth's elliptical orbit.

So the analemma captures the Sun sometimes earlier than, and sometimes

later than, what would be the theoretical 'average' position of the Sun (sometimes called "Mean Sun") over the course of a year.

The analemma doesn't actually 'exist' as a physical reality. For those who are not familiar with the term, this is how you would 'observe' the analemma. Set up a camera in such a way that it will capture an image of the Sun at, for example, exactly 12:00 noon, in your local timezone.

Keep the camera firmly anchored and under enough protection so that it can remain where it is for an entire year. At regular weekly intervals photograph the Sun at exactly 12:00 noon. At the end of the year, the image will show the characteristic "8" shape of the analemma. The one thing you will have to do is assure that the initial camera's view is such that the Sun will always appear in the image at noontime, all year. If you start with the Sun exactly in the middle, there may be a season when the Sun at noon will not be in the camera's view.

Also you need to allow for "daylight saving" changes to your local noon, of course.