Plot the variation between the mean Sun and apparent Sun over the course of a year
The real or apparent Sun oscillates in position either side of the mean Sun
There are two Suns in our sky – one is real and one conceptual. The conceptual or ‘mean’ Sun is important because it allows us to stabilise the length of our days. The real or apparent Sun oscillates in position either side of the mean Sun, and this is what we are attempting to reveal for this month’s challenge. Actually, this will take more than a month – it’ll take a year!
The apparent speed of the real Sun in the sky varies over the course of a year due to two effects – the axial tilt (obliquity) and orbital ellipticity of Earth. These affect the apparent position of the Sun, their combined effects generating a value known as the ‘Equation of Time’. This oddly named commodity varies in value over the year. Apparent time can become 16m33s ahead of clock time around 3 November or 14m06s behind it around 11 February. Apparent time and clock time only match (when the Equation of Time = 00m00s) around 15 April, 13 June, 1 September and 25 December.
The mean Sun represents the position of the Sun corrected for the Equation of Time. For example, the mean Sun always sits due south at midday UT, while the apparent Sun mostly doesn’t, depending on the date and the prevailing value of the Equation of Time. If you have a patient disposition, the variation can be shown using a gnomon, basically a shadow casting stick or structure. Ideally, the shadow needs to fall on a large flat area.
All you need to do is mark the position of the gnomon’s shadow tip at the same UT time of day over the course of a year.
In reality this won’t be possible due to life events and the weather of course, but this shouldn’t be an issue as long as you can create one shadow mark at least approximately every 10–14 days. How you make each mark is up to you, but be aware they need to survive the rigours of being outdoors for at least a year.
Location is important. Consider where the shadow will fall over the course of the year. Midday UT is a good time to aim for, but make sure the Sun doesn’t get blocked by foreground structures near the December solstice when it’ll appear lowest in the sky.
If you manage to see this long-term project through, the pattern revealed may surprise you. The plot shows the solar analemma, a shape reminiscent of a bowling pin. This is the physical depiction of the Equation of Time, a direct representation of how Earth’s axis and orbit affects the real position of the Sun in our sky.