The elevation and the azimuth of the sun changes throughout the year, varying in essentially a sine wave pattern with a full wave occurring in a one year period.

For determining the solstice, one is interested only in the few days surrounding the solstice.

Further, there is no need to have detailed numerical measurements. The only information of interest is when the rate of change stops, and starts to turn in the other direction.

The following charts show the elevation and azimuth of the sun for December 18 to 25, 2006.

Note that the peak azimuth would be approximately 42.5 if the two legs of the curve were extended together in the center. Also note that each graph would suggest a slightly different peak/minimum. This is because the values are quite small, and are within the error caused by providing only average data for a single day.

Select DATA TABLE from the menu to view the data used for these graphs.

From these graphs it can be seen that the change in elevation or azimuth for the one day period before and after the instant of the solstice is about 1/2 arc minute. (An angle of one arc degree = 60 arc minutes.)

Extending this to the two day period before and after the instant of the solstice gives approximately one arc minute.

Thus the accuracy of any determination of the specific day of the solstice depends upon the accuracy of observations that are done, i.e. on the order of 1/2 arc minute for a specific day and 1 arc minute for sometime within a 3-4 day period.

It should also be noted that, while the elevation of the sun at mid-day is rather constant for the short minute or two required to make a daily observation, the azimuth of the sun changes as the sun rises (or sets), making the time available for making azimuth observations considerably shorter if it is observed on a flat horizon. If observed on a properly slanted distant horizon the time may be substantially longer.

There is one exception. Repeating the observations over several years (centuries?) and averaging the plots would likely improve the accuracy of the specific day selected for the solstice. This was likely done by the ancients in determining where to set their viewing markers. Having set their markers, they only needed to limit the slice of the sun that they could view to that which would only appear on one day. (The Newgrange, Ireland site views a significantly larger slice of the sun, and determines a solstice period of six days rather than a single solstice day.)