Sundial - Apparent Motion of The Sun

Apparent Motion of The Sun

The principles of sundials can be understood most easily from the Sun's apparent motion. Scientists have proven that the Earth rotates on its axis, and revolves in an elliptic orbit about the Sun; however, meticulous observations and experiments were needed. For the purposes of a sundial, an excellent approximation assumes that the Sun revolves around a stationary Earth on the celestial sphere, which rotates every 23 hours and 56 minutes about its celestial axis. The celestial axis is the line connecting the celestial poles. Since the celestial axis is aligned with the axis about which the Earth rotates, the angle of the axis with the local horizontal is the local geographical latitude.

Unlike the fixed stars, the Sun changes its position on the celestial sphere, being at a positive declination in summer, at a negative declination in winter, and having exactly zero declination (i.e., being on the celestial equator) at the equinoxes. The Sun's celestial longitude also varies, changing by one complete revolution per year. The path of the Sun on the celestial sphere is called the ecliptic. The ecliptic passes through the twelve constellations of the zodiac in the course of a year.

This model of the Sun's motion helps to understand sundials. If the shadow-casting gnomon is aligned with the celestial poles, its shadow will revolve at a constant rate, and this rotation will not change with the seasons. This is the most common design. In such cases, the same hour lines may be used throughout the year. The hour-lines will be spaced uniformly if the surface receiving the shadow is either perpendicular (as in the equatorial sundial) or circular about the gnomon (as in the armillary sphere).

In other cases, the hour-lines are not spaced evenly, even though the shadow rotates uniformly. If the gnomon is not aligned with the celestial poles, even its shadow will not rotate uniformly, and the hour lines must be corrected accordingly. The rays of light that graze the tip of a gnomon, or which pass through a small hole, or reflect from a small mirror, trace out a cone aligned with the celestial poles. The corresponding light-spot or shadow-tip, if it falls onto a flat surface, will trace out a conic section, such as a hyperbola, ellipse or (at the North or South Poles) a circle.

This conic section is the intersection of the cone of light rays with the flat surface. This cone and its conic section change with the seasons, as the Sun's declination changes; hence, sundials that follow the motion of such light-spots or shadow-tips often have different hour-lines for different times of the year. This is seen in shepherd's dials, sundial rings, and vertical gnomons such as obelisks. Alternatively, sundials may change the angle and/or position of the gnomon relative to the hour lines, as in the analemmatic dial or the Lambert dial.