# How does the appearance of the analemma vary with latitude

How does the appearance of an analemma vary with latitude?

This what I take to be a definition of an analemma: If the position of the sun is plotted or photographed at noon clock time (say UTC) every day from a position facing due south (in the northern hemisphere) it forms a figure of eight shape as in the picture.

Photographs usually show it with the long axis at an angle. My question is, assuming that the angle is related to the latitude of the camera, how does this angle vary as the camera is moved from the equator to the pole, and why?

Analemma is a diagram showing the deviation of the Sun from its mean motion in the sky, as viewed from a fixed location on the Earth. Note that it says nothing about time- it can be any fixed time. Analemmas created at different times of the day have slightly different shapes. For example, see the solar analemmas taken at the same place at different times.

Solar analemma at 0700 UTC by Anthony Ayiomamitis, from solar-center.stanford.edu

Solar analemma at 1400 UTC by Anthony Ayiomamitis, from solar-center.stanford.edu

The best way to understand the effect of latitude on the shape of the analemma is to consider the effect of earth's axial tilt on the shape of the analemma.

If the Earth’s orbital path was elliptical, but its axis was not tilted, the 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.

The 23.5-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 an 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.

You're correct that the tilt of the analemma varies with the latitude. Observers in the Northern hemisphere will obtain an analemma curve with the broader loop at the bottom. This reverses for observers in the Southern hemisphere, where the broader loop is on the top of the curve. At equator, the anlaemma lies on its side. At north pole, only the top of the analemma would be visible, while it is the opposite at the south pole.

• Thanks @aeroalias, that is a very nice answer, and I have accepted it over my own because of the trouble taken. I realise now that it all depends on what you mean by the "shape". It will appear different in photographs because of the impossibility of reproducing a curved object on a flat surface. I believe that the shape measured in degrees of latitude relative to the equator and longitude either side of due south will be the same wherever it is viewed.See the Wikipedia article and in particular: en.wikipedia.org/wiki/Analemma#/media/File:Analemma_Earth.png – Harry Weston Nov 25 '15 at 15:19

It is an effect caused by the inclination of the precession axis. This axis takes about 23,000 years to complete. If we could live so long we would see the anemalema spinning in the sky

I think that the answer is that the analemma would always be vertical, at right angles to the equator, if photographed at midday. The apparent slope in photographs is due to perspective, and being taken at a different time of day, not at noon.

At the equator the analemma will be directly overhead at the equinoxes, and off this by the angle of the ecliptic at the solstices.

At the poles the analemma will be centred on the horizon, the top half giving the long period without night in the summer, and the obscured half the long winters without daylight.