Editing Sundial (section)

==Apparent motion of the Sun==
[[File:Equatorial sundial topview.gif|thumb|Top view of an equatorial sundial. The hour lines are spaced equally about the circle, and the shadow of the gnomon (a thin cylindrical rod) moving from 3:00{{spaces}}a.m. to 9:00{{spaces}}p.m. on or around [[Solstice]], when the Sun is at its highest [[declination]].]]
The principles of sundials are understood most easily from the [[Sun]]'s apparent motion.<ref>{{Cite book|url=https://books.google.com/books?id=cAFEAgAAQBAJ&q=The+principles+of+sundials+are+understood+most+easily+from+the+Sun%27s+apparent+motion.&pg=PA52|title=Using Network and Mobile Technology to Bridge Formal and Informal Learning|last1=Trentin|first1=Guglielmo|last2=Repetto|first2=Manuela|date=2013-02-08|publisher=Elsevier|isbn=9781780633626|language=en|access-date=2020-10-20|archive-date=2023-04-21|archive-url=https://web.archive.org/web/20230421080805/https://books.google.com/books?id=cAFEAgAAQBAJ&q=The+principles+of+sundials+are+understood+most+easily+from+the+Sun%27s+apparent+motion.&pg=PA52|url-status=live}}</ref> The Earth rotates on its axis, and revolves in an elliptical orbit around the Sun. An excellent approximation assumes that the Sun revolves around a stationary Earth on the [[celestial sphere]], which rotates every 24 hours about its celestial axis. The celestial axis is the line connecting the [[celestial pole]]s. 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 (in the northern hemisphere) at a positive [[declination]] in spring and summer, and at a negative declination in autumn and winter, and having exactly zero declination (i.e., being on the [[celestial equator]]) at the [[equinox]]es. 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.

[[File:Sundial, Singapore Botanic Gardens.jpg|thumb|left|Bowstring sundial in [[Singapore Botanic Gardens]]. The design shows that [[Singapore]] is located almost at the [[equator]].]]

This model of the Sun's motion helps to understand sundials. If the shadow-casting gnomon is aligned with the [[celestial pole]]s, 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 (geometry)|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 or position (or both) of the gnomon relative to the hour lines, as in the analemmatic dial or the Lambert dial.