## Solar Date Determination

By "solar date" we mean the location of the Sun along the ecliptic, its annual path. The celestial longitude of the Sun will increase from day to day, although, as noted in §3.1.1, the rate varies over the course of the year. Differing positions on the ecliptic (i.e., different celestial longitudes) correspond to differing declinations as well as differing right ascensions. The variation in declination means that the Sun's meridian altitude—its altitude when it crosses the celestial meridian—will vary also during the year. Figure 3.17 shows that the meridian altitude of an object, the declination of which is known, can provide the latitude of the observer, by the expression hm = 90 0 - (f - 5), (4.16)

where f is the latitude of the observer and 5 is the declination of the Sun. In this equation, 5 carries its own sign so that when the Sun is at southern (i.e., negative) declinations, hm = 90° - (f + 151). To derive (4.16), consult Figure 3.17a and b.

The tower of Chou Kung, near Loyang, China, contains a 12-m gnomon that casts its noon shadow along a horizontal stone terrace that was marked by a scale (Needham 1981, Figs. 80-82). Such a device constitutes a solar calendar, capable of marking the passage of the days of the year, at the same time that it provides the instant of local noon.

Indeed, not only at noon, but at any given time of day, the altitude will change from one day to the next. The altitude of the Sun determines the length of the shadow. An historic example of the use of shadow lengths at particular times of day can be seen on the faces of the Tower of Winds (Figure 4.3; §7.3). Twice a year (except at each solstice) the Sun will

 Type of year Length (mean solar days) Variation Anomalistic 365d25964134 = 365d06h13m53.0 0dGGGGG3G4T Sidereal 365.25636556 = 365 06 09 09.98
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