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a The year lasts slightly more than 365 civil days (the numbers of days as recorded by civil authorities), requiring the inclusion of an extra day almost every 4 years to keep the calendar in step with the astronomical seasons.

a The year lasts slightly more than 365 civil days (the numbers of days as recorded by civil authorities), requiring the inclusion of an extra day almost every 4 years to keep the calendar in step with the astronomical seasons.

sphere) seasons for three important epochs among others tabulated by Meeus (1983b) are shown in Table 2.3.

Now we can tie in the motions of the Sun to the seasonal visibility of asterisms. Because the Sun must cover 360° in the course of a year, it must move eastward at slightly less than 1°/day on average. As a consequence, the groups of stars that can be seen during the night, change slowly from night to night, amounting to an angular displacement of about 1/12 of the sky's circumference or 30° in a month. Suppose a particular group of stars on the celestial equator will be seen to rise at sunset; 10 days later, another group of stars about 10° to the east will appear to rise at that time. In the same interval, the stars in the westernmost 10° will disappear in the evening twilight. Figure 2.11 compares the constellations on the meridian at evening twilight, but two months apart. Over the course of a year, Hesiod's seasonal signs follow. The Egyptians used asterisms to keep track of hours, days, months, and, indeed, years! (See §4.) These decans19 were about 10° apart.

The seasonal variation of the Sun in both right ascension and declination creates an interesting pattern in the sky over the course of the year. The Sun's eastward motion, combined with its apparent northern motion from winter to summer (and southern motion from summer to winter), appears to spiral through the sky; some cultures saw the weaving of a pattern. With sufficient patience and endurance, it can be demonstrated! A camera recording the noon position of the Sun a regular number of days apart over the course of a year will produce a figure-eight pattern called an analemma. This figure marks the variation in the Sun's instant of arrival at the meridian and its variation in declination, and so it is a marker of the seasons and of solar time. It will be discussed in later chapters (e.g., §4.1.1.2) for both reasons. For many cultures, from Britain to Egypt, the return of the Sun from its winter quarters and its return from darkness every morning were direct analogs of an endless cycle of death and rebirth. As such, they became mystical, religious events to be observed and celebrated and, in the highest plane of the human spirit, appropriated.

19 The decans were depicted as two-legged beings, sentries guarding the portals of the night. From the tomb of Seti I (~1350 b.c.) (Neugebauer and Parker, 1969, plate 3).

Figure 2.11. Simulation of constellations centered on the meridian at the same mean solar time in the evening (2100 MST), but two months apart: (a) Jan. 24, 1985, (b) Mar. 24, 1985, as seen from Calgary, Alberta. The equatorial grid is shown with the solid line, with declinations indicated on the extreme right and a few right ascensions at the bottom. The

Figure 2.11. Simulation of constellations centered on the meridian at the same mean solar time in the evening (2100 MST), but two months apart: (a) Jan. 24, 1985, (b) Mar. 24, 1985, as seen from Calgary, Alberta. The equatorial grid is shown with the solid line, with declinations indicated on the extreme right and a few right ascensions at the bottom. The ecliptic is shown arching across the field. The horizon grid is shown with a lightly broken line, with altitudes indicated on the extreme left and a pair of azimuths marked on the vertical circle arcs radiating from the zenith. Produced by E.F. Milone with TheSky software package (Software Bisque, Golden, CO).

2.3.2. The Zodiac

The Sun's annual journey involves visits to successive areas of the sky. Twelve constellations follow one another in a band around the sky. They straddle the ecliptic, the path of the Sun during its annual journey among the stars. The band of constellations is called the zodiac, from the Greek ZwStaKÔç kîikIoç (zodiacos kuklos), "circle of the animals"). The naming of most of the zodiacal constellations took place in Mesopotamia. According to Neugebauer (1969, p. 102ff), the subsequent assignment of the zodiacal constellation names to a series of 30° segments of the sky along the ecliptic was probably first carried out in the 4th century b.c. (for alternative views, see §7.1.2.3). The uniform lengths of exactly 30° each created a longitude-like coordinate by which positions could be assigned to the stars. These

12 constellations were thus turned into signs.20 The Greco-Roman zodiac (with the symbol for each sign) is shown with the Mesopotamian and Indian equivalents in Table 2.4, in the order in which they are visited by the Sun during the year. This is also the order in which the constellations rise and the order of increasing right ascension. The series starts

20 A similar shift from 28 (sometimes 27) zodiacal asterisms (representing lunar "houses," "lodges," or "mansions," that is, places for the Moon to "stay" among the stars during its monthly sojourn around the Earth), to 27 signs, beginning with the vernal equinox, occurred in India.

with Aries and progresses eastward. Although the attested date of the zodiac's origin is late, the fact that the spring equinox was actually in Aries between 2000 and 100 b.c. provides evidence for a much earlier, if undocumented, usage. The boundaries of the modern zodiacal constellations as established by the International Astronomical Union are not uniform in extent, but the boundaries of the zo diacal signs are. Each zodiacal sign is 18° high, centered on the ecliptic. The Greeks fixed the widths of each of the signs at 30°. The zodiac had an important mathematical use in the ancient world: The number of degrees from the beginning of each sign was used to record planetary positions. This measurement scheme, in use in Ptolemy's

Table 2.4. Zodiacal constellations.

Latin

(Ptolemaic)

Babylonian

Indian

Symbol

Celestial/ ecliptic longitude8

Aries

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