Calculating solar noon requires only three simple tools: a square mirror, a watch and a writing implement. If one has access to a sunlit window, place a mirror to project the Sun's image onto a wall or ceiling. At local noon each day, mark this image with a dot. Over the course of a year a figure eight pattern emerges.
This figure eight pattern, called an analemma, is printed on most globes over the eastern Pacific Ocean. Examining this figure more closely reveals that, for most of the year, clock time and sun time are not identical. For observers in the Northern Hemisphere, the local time at noon lags behind solar noon from mid-April through late June and from September through the winter solstice. Conversely local time runs ahead of solar noon, from late December to mid-April and from the June solstice through August.
The two times coincide four days each year: the summer and winter solstices, three weeks prior to the autumnal equinox and three weeks after the vernal equinox. The basis of this time discrepancy is twofold. First, the shape of Earth's orbit around the sun is elliptical, not circular. Second, the Earth's rotational axis is tilted at a 23.5 degree angle, with respect to the sun. If Earth's rotational axis were perpendicular to its orbit, day and night would be of equal length all year and there would be no seasons. .